For the same reason we don't kill ourselves to get to heaven.

For example, it's one thing to give up your life for another. It's another thing to kill yourself for another. Taking your own life is a sin.

Lot couldn't offer himself. That would have been a sin. But he was willing to give up what was most precious to him - his own flesh and blood. Not that the men of Sodom wanted him or his daughters anyways. Lot was a sojourner among them, meaning he lived with them but he wasn't one of them. They could have insisted on having sex with them long before the angels arrived.

The men of Sodom wanted to know the angels.

Ask yourself one question. If a bunch of women wanted to have sex with you, how much resistance would you put up? It depends on the man. Some men would welcome the chance to have sex with them. Others would say no. If they were forced, then we would call it rape. The same thing applies to women. Some women will have multiple sex partners and enjoy it but if they are forced, then we would call it rape.

Now imagine a society without any law against sex. In this society, having sex is as common as two people shaking hands. In fact, it is considered rude and impolite to refuse to have sex. Not that they force anyone. No. They're not rapists. However, they do consider it rude, impolite, and even selfish to refuse pleasure when it is offered....