You said marriage is not obligated but we’re told it’s half of the deen
The “half our deen” saying comes from a group of hadith narrations all of which are of questionable authenticity. One of them comes from al-Bayhaqi’s collection and the chain of narrators includes يزيد الرقاشي, who is untrustworthy according to al-Tirmidhi and Ibn Hajar. Another version comes from al-Hakim’s collection, and the chain contains عبد الرحمن بن زيد, who is untrustworthy.
There is another famous saying “a woman completes part of a man’s faith”, this is not from the Prophet, but from Tawus ibn Kaysan, it is just a scholar speaking his personal opinion.
The hadith scholar al-Albani does a detailed study and considers all of the narrations untrustworthy except one that says “A woman supports a man in part of his deed, so let him worry about the second part.” This hadith is not authentic due to its chain containing at least one person whose is known to be of arbitrary reliability (he sometimes speaks the truth, sometimes says something completely wrong). al-Albani concludes that the hadith has a status of “hasan”, meaning that it is not authentic (”saheeh”), but that the content and the chain of narrations is good enough that one cannot say with certainty that it is fabricated (”dha`eef” or “maudhoo`”).
In conclusion, therefore, this “half our deen” concept is not certain and cannot be used as a basis for deriving principles. Since it sounds good, most people, including clerics and scholars, have accepted it without questioning. It sounds nice, and you can’t question nice things, otherwise that makes you a mean person.
I rarely hear a Friday sermon in which the preacher does not mention some cringe-worthy false narration. It is for the greater good, so even if they know the hadith is fabricated, the preacher believes that the end justifies the means. Even if it is a lie, it sounds good and is supposedly beneficial, so they repeat it.
One commonly repeated false saying that non-Muslims have used for the past century to poke fun at Islam is that a martyr is given 72 virgins in Paradise, and this is repeated by some Muslims to this day. This is from a set of weak hadith narrations whose chains of narrators cannot warrant a higher status than dhaeef (”weak”, i.e. unauthentic) (see Apppendix IV of Jonathan Brown’s Misquoting Muhammad). God, of course, has the power to reward people however He wants, but since these narrations are false, they are false, therefore Muslims must stop repeating them even if they are considered useful. A lie is a lie regardless of how useful someone thinks it is.