The issue of whether making pictures or paintings of living things (taṣwīr) is permitted in Islam has led to a great amount of controversy. Mainstream scholars (such as those of al-Azhar University) have chosen to permit it due to considering the evidence for the prohibition not strong enough, while those who consider themselves true followers of hadith have chosen to accept the prohibition. There are also important exceptions, such as the Syrian Shaykh Muhammad b. Amin, a follower of Ibn Tamiyya, who also considers the evidence for the prohibition unsatisfactory and contradictory. See my translation of an important article by him: A Traditionalist Critique of the Islamic Prohibition on Taṣwīr (Making Drawings and Statues of Humans and Animals).
I decided to conduct a study of the existing hadith evidence to find out its strength using the probabilistic hadith criticism method. The result, as I expected, is that none of the hadiths are strong enough to establish the prohibition, and there is one hadith among them that demolishes the rest. Unfortunately this hadith too is not very strong, although this can be explained by hadith scholars choosing to ignore it and not transmit it due to conflicting with their own views. But the hadith’s content happens to be the most believable compared to the rest due to the way it mentions a very realistic scenario. The quality of the hadith’s content is very similar to the strongest hadiths we have.
I ignored hadiths that merely mention that al-muṣawwirūn are punished by God due to the fact that these hadiths could simply be referring to those who make icons and statues meant for worship. The hadiths I included are those that seem to clearly imply that all picture-making is prohibited regardless of the intention behind making them.
Hadith 1
Narrated Ibn Umar:
Allah's Messenger (ﷺ) said, "Those who make these pictures will be punished on the Day of Resurrection, and it will be said to them. 'Make alive what you have created.'
Sahih al-Bukhari 5951, also in Musnad
Below is a diagram of the hadith’s chains:
The hadith receives an authenticity score of 16%, which is far below the 30% needed for ruling it ṣaḥīḥ (authentic) according to the probabilistic verification methodology. (This article contains a guide on how to do these calculations).
Hadith 2
I heard [Prophet] Muhammad saying, "Whoever makes a picture in this world will be asked to put life into it on the Day of Resurrection, but he will not be able to do so."
Sahih al-Bukhari 5963, also in Muslim, Musnad, al-Tabarni, Musnad Abi Ya`la, al-Bayhaqi and al-Nasa'i.
Below is the diagram of its chains:
This hadith, despite its convoluted chains, receives an authenticity score of 19.44%.
Hadith 3
I heard from Allah's Messenger (ﷺ). I heard him say: All the painters who make pictures would be in the fire of Hell. The soul will be breathed in every picture prepared by him and it shall punish him in Hell ...
Sahih Muslim 2109 c, 2110 a, Musnad
Below is the chain diagram:
This hadith has a score of 8.6%, making it rather weak.
Hadith 4
Narrated `Aisha:
I purchased a cushion with pictures on it. The Prophet (came and) stood at the door but did not enter. I said (to him), "I repent to Allah for what (the guilt) I have done." He said, "What is this cushion?" I said, "It is for you to sit on and recline on." He said, "The makers of these pictures will be punished on the Day of Resurrection and it will be said to them, 'Make alive what you have created.' Moreover, the angels do not enter a house where there are pictures.'"
Sahih al-Bukhari 5957, the strongest chain is in al-Muwatta
Chain diagram:
This hadith has a score of 21.6%, again below 30%.
Hadith 5
Narrated `Aisha:
Allah's Messenger (ﷺ) returned from a journey when I had placed a curtain of mine having pictures over (the door of) a chamber of mine. When Allah's Messenger (ﷺ) saw it, he tore it and said, "The people who will receive the severest punishment on the Day of Resurrection will be those who try to make the like of Allah's creations." So we turned it (i.e., the curtain) into one or two cushions.
Sahih al-Bukhari 5954, also in Muslim
Chain diagram:
This hadith gets a score of 10.1%.
Hadith 6
Narrated Abu Zur'a:
l entered a house in Medina with Abu Huraira, and he saw a man making pictures at the top of the house. Abu Huraira said, "I heard Allah's Messenger (ﷺ) saying that Allah said, 'Who would be more unjust than the one who tries to create the like of My creatures? Let them create a grain: let them create a gnat.' "Abu Huraira then asked for a water container and washed his arms up to his armpits. I said, "Abu Huraira! Is this something you have heard I from Allah's Messenger (ﷺ)?" He said, "The limit for ablution is up to the place where the ornaments will reach on the Day of Resurrection.'
Sahih al-Bukhari 5953, also in Musnad Ishaq b. Rahawayh
Chain diagram:
This hadith gets a score of 11.5%.
Hadith 7
This is the hadith that refutes the others, in which Aisha (may God be pleased with her) denies having said that angels do not enter a house in which there is a picture (Hadith 4 above).
Abu Talha Ansari reported Allah's Messenger (ﷺ) as saying:
Angels do not enter the house in which there is a picture or portraits. I came to 'A'isha and said to her: This is a news that I have received that Allah's Apostle (ﷺ) had said: Angels do not enter the house in which there is a picture or a dog, (and further added) whether she had heard Allah's Messenger (ﷺ) making a mention of it. She said: No (I did not hear this myself), but I narrate to you what I saw him doing. I bear testimony to the fact that he (the Holy Prophet) set out for an expedition. I took a carpet and screened the door with it. When he (the Holy Prophet) came back he saw that carpet and I perceived signs of disapproval on his face. He pulled it until it was torn or it was cut (into pieces) and he said: God has not commanded us to clothe stones and clay. We cut it (the curtain) and prepared two pillows out of it by stuffing them with the fibre of date-palms and he (the Holy Prophet) did not find fault with it.
Sahih Muslim 2106 f, 2107 a
Chain diagram:
This hadith gets a score of only 3.25% due to the lack of supporting chains, although the first three transmitters are all Companions. If we assume that all three transmitted the hadith with complete authenticity, the hadith’s score rises to 9.03%, which is still not very good.
Hadith 8
We also have the following hadith (considered authentic by al-Albani) in which we find Aisha had toy horses that had wings.
Narrated Aisha:
When the Messenger of Allah (ﷺ) arrived after the expedition to Tabuk or Khaybar (the narrator is doubtful), the draught raised an end of a curtain which was hung in front of her store-room, revealing some dolls which belonged to her.
He asked: What is this? She replied: My dolls. Among them he saw a horse with wings made of rags, and asked: What is this I see among them? She replied: A horse. He asked: What is this that it has on it? She replied: Two wings. He asked: A horse with two wings? She replied: Have you not heard that Solomon had horses with wings? She said: Thereupon the Messenger of Allah (ﷺ) laughed so heartily that I could see his molar teeth.
Sunan Abi Dawud 4932
Chain diagram:
This chain gets a score of 1.4%, again due to the lack of supporting chains. But again its contents seem extremely realistic. My heart is much happier with this kind of hadith that mentions a lot of contextual and seemingly unnecessary details than with hadiths that merely transmit a statement of the Prophet 
.
What we can conclude
It looks like the instinct of the Azhar scholars is correct in not taking the prohibitory hadiths too seriously. Real prohibitions in Islam have extremely strong support behind them, with hadiths easily reaching 80% or 90% authenticity. The strongest prohibitory hadith only reaches a score of 21.6%.
The question is why the Prophet failed to impart this prohibition to his followers like normal prohibitions. Why did it have to come to us through isolated and rather low-quality hadiths? The most likely answer is that because he never taught such a prohibition. It seems very likely that the culture of the generation of Imam Malik began to confuse the hadiths in which the Prophet spoke strongly against picture-making meant for worship (i.e. idol-making), so that the context was lost and only the part where he mentioned picture-making survived. A prohibition on making religious idols became generalized in people’s minds to a prohibition on all picture-making.
Shaykh Ibn Amin’s study (that I linked earlier) adds further support to this theory. The Companions seem to have had a very casual attitude toward pictures and statues. We also know that Prophet Sulayman had statues built for him as the Quran tells us. The evidence of the Quran is always much stronger than hadith (due to the Quran’s far better transmission process), so the Quranic verse can be taken as strong evidence for the permissibility of picture-making (and even statues). The hadiths mentioned above are rather low-quality to be able to override what the Quran tells us.
We also know that one of the most respected early scholars of Islam (from the generation before Imam Malik) approved of picture-making (al-Qasim b. Muhammad).
The two hadiths of Aisha are also highly suggestive. In both of them the Prophet does not criticize the pictures/statues. In the first one he criticizes using cloth to cover walls, and in the second one he laughs at the toy horse without criticizing it.
There is also a place for human reason in this debate. It seems ridiculous to consider paintings of birds and animals as some sort of insult against God when in our daily lives we feel absolutely no compunction about things like children’s picture books filled with such paintings and drawings. The Quran tells us that the creation of the heavens and the earth is a greater accomplishment than the creation of humans (verse 40:57), so why should God feel jealous about painting humans and animals but not about painting stars and landscapes (which are God’s greater creation)?
All of Islam’s prohibitions seem to have some sense behind them, or they have very strong Quranic evidence. But in this case the evidence for the prohibition is rather weak and contradictory, and our own reason and conscience find no good justification for it.
Unfortunately we are stuck in this position where we have many low-quality hadiths creating a taboo against paintings and statues, and some (also weak) evidence going against the taboo. We also have the Quranic statement approving of Prophet Sulayman’s statues. So it seems that Muslims will forever have to deal with the ambiguities and uncertainty surrounding the issue, with mainstream scholars taking a tolerant attitude and a minority taking an extreme position in support of the taboo.
My conclusion
My own stance is to fully approve of drawings and paintings of living things, and as for statues, I consider them at worst to be in a gray area. I see no strong Islamic justification for speaking against those who make them.