When prophet Lut alaysalam asked the people of his time and offered his daughters in marriage for them, what was the reason or thought process behind this, if those people were attracted to men, and please advise what the wisdom behind this is

His daughters here means the women of his people, because a prophet is like a father to his nation, and he was calling them to marry them lawfully in place of their filth, not permitting anything forbidden, as the Permanent Committee explained. Some scholars said he meant his own daughters.