What is something that you just don't understand about the Christian faith?

There is a lot to unpack here. We are not told Lot's exact reasons for being willing to give his daughters to protect the angels, although it may be to do with customs in that society concerning the treatment of guests (and the contrasting treatment of women in that society). Nothing in scripture indicates that Lot's proposed course of action here was morally correct, and that he is flawed in this way is evidence towards the fallen nature of humans.

The only place where Lot is referred to as righteous is in 2 Peter 2:7-8, where the focus is on giving old testament examples where God judges the wicked but is able to rescue the godly, in the face of false teachers infiltrating the church. There the point that is made is not that Lot was righteous in offering up his daughters, but that during the time he lived in Sodom he had a very different moral outlook to the people among whom he lived. It is stated that he was oppressed or troubled by seeing the deeds of the people he dwelt among, and that may include the effect it has on his own soul in moving him to accept the attitudes of those around him (which we see play out in the incident where he offers up his daughters). No clear mention is made of the circumstances or reasons for Lot's being brought out of Sodom in 2 Peter.

The clearest statement we see in scripture as to why Lot was saved when Sodom was destroyed is in Genesis 19:29, where it says that God remembered Abraham. So Lot's salvation rests not on his righteousness, but on Abraham's intercession in Genesis 18:22-33 and God's mercy to him. The connection to Abraham is particularly important because Abraham is the one to whom God's promises are made, and who therefore constitutes God's covenant people at this point in biblical history. Lot's leaving Abraham in Genesis 13 is the start of a series of bad choices that separate him from God's people. Indeed, by the end of Genesis 19 we see Lot has fallen to an incident of incest with his daughters, and the descendants of this are the Ammonites and Moabites, who become significant enemies of God's people.

You should not assume that just because something is recorded in scripture (particularly in the narrative portions), that it is something that God supports. A large part of scripture is detailing the history of God's people, who are not always as righteous as they should be, and pointing to our need for a saviour, sometimes through the examples of sins from which we must be saved.

Similarly, since everyone except Jesus is sinful, we see even the most righteous people with flaws. This is particularly seen in the books of Kings and Chronicles where we see kings with the verdict that they did what was right sometimes doing bad things. To give some examples: David did what is right (1 Kings 15:5) and held up as a standard against which other kings of Judah are compared, but he sinned in committing adultery with Bathsheba (2 Samuel 11). Solomon was renowned for his wisdom (1 Kings 4:29-34) and he built the temple, but he married women from the surrounding nations and ended up worshipping their gods (1 Kings 11:1-8), so we are told he did what was evil in God's sight (1 Kings 11:6). Asa did what was right (1 Kings 15:11) in removing pagan worship, but he did not do it completely (1 Kings 15:14), and he used treasures from the temple to buy the allegiance of Syria (1 Kings 15:18-19). Joash did what was right during the life of Jehoiada the priest (2 Chronicles 24:2), but turns from God after his death (2 Chronicles 24:17-19). Uzziah did what was right (2 Chronicles 26:4), but became prideful and sinned (2 Chronicles 26:16).

The bible teaches that men may never be subjugated like a woman, through a story of violence. It's also why homosexuality is considered morally wrong.

As I've explained above, that isn't what is being taught in the story of Lot, and it isn't an analysis of the event that is presented anywhere else in the Bible. I would like expand on the point about homosexuality though. The Bible's reasoning concerning homosexuality has nothing to do with any notion of "men being subjugated like women", particularly since such a line of reasoning could only really apply to male homosexuality. Rather, the reasoning is simply that it is not part God's plan for how human sexual relations should be, but that people are given over to them because of their rejection of God (Romans 1:24-27).

Not only that, women aren't allowed to reject their husbands sexual advances, rendering marital rape null. Even if the marriage was arranged outside of her say.

This is a separate point, and it doesn't come from any strict requirement in the old testament law, but from the advice given in 1 Corinthians 7:3-5. There the advice is given equally to both husbands and wives, and does not licence the use of coercion or force in sexual relations with one's spouse. Here, Paul is responding to the statement in 1 Corinthians 7:1, which is that husbands should avoid all sexual relations, and Paul's response is that sexual relations within marriage are not wrong and that it is even good to have sexual relations to avoid outside temptation to sexual sin. What seems to be in view here is particularly a marriage where both spouses are Christians, and it is assumed they would both behave as expected of Christians in marriage, particularly the husband loving his wife as Christ loved the Church (Ephesians 5:25-33). A man not behaving in such a way towards his wife would come under church discipline. Of course, there are marriages where the husband may not be a Christian, but the same principles apply so any violence or coercion would not be right.