What follows is a reading of the Sodom narrative based on the commentary of Nachmanides which is drastically different from the way this story is commonly understood. No other reading of this story makes sense to me.
Progression of events:
The people of Sodom gather outside Lot's house and they make a request. The original Hebrew is highly ambiguous here:
וַיִּקְרְאוּ אֶל-לוֹט וַיֹּאמְרוּ לוֹ, אַיֵּה הָאֲנָשִׁים
אֲשֶׁר-בָּאוּ אֵלֶיךָ הַלָּיְלָה; הוֹצִיאֵם אֵלֵינוּ, וְנֵדְעָה אֹתָם.
5 And they called unto Lot, and said unto him: 'Where are the men that
came in to thee this night? bring them out unto us, that we may know
In both English and Hebrew, the word "know" can be understood here in a cognitive or sexual sense. Lot responds to this request by offering the people of Sodom his two daughters:
"do to them as is good in your eyes;"
The townspeople are infuriated by Lot's offer and they respond:
יט,ט וַיֹּאמְרוּ גֶּשׁ-הָלְאָה, וַיֹּאמְרוּ הָאֶחָד בָּא-לָגוּר
וַיִּשְׁפֹּט שָׁפוֹט--עַתָּה, נָרַע לְךָ מֵהֶם
'This one fellow [Lot] came in to sojourn, and he will needs play the
judge; now will we deal worse with thee, than with them.'
It's clear from their response that the townspeople have no interest in Lot's daughters and that the offer was highly offensive to them. In my opinion, the Sodomites wanted to expel Lot's visitors from the city for any number of social/economic reasons and their justification: "that we may know them," is a thinly veiled threat, like saying: "we just want to talk." "That we may know them" also serves to highlight that these people are outsiders of the town that no one knows. Of course Lot understands the intentions of the mob and so he mocks them for their cruelty by intentionally misunderstanding their previous statement to suggest that the people want to engage in gang rape and sodomy:
ט,ז וַיֹּאמַר: אַל-נָא אַחַי, תָּרֵעוּ. יט,ח הִנֵּה-נָא לִי שְׁתֵּי
בָנוֹת, אֲשֶׁר לֹא-יָדְעוּ אִישׁ--אוֹצִיאָה-נָּא אֶתְהֶן אֲלֵיכֶם,
וַעֲשׂוּ לָהֶן כַּטּוֹב בְּעֵינֵיכֶם
7 And he said: 'I pray you, my brethren, do not so wickedly. 8 Behold
now, I have two daughters that have not known man; let me, I pray you,
bring them out unto you, and do ye to them as is good in your eyes;
Lot would never give over his daughters to the people of Sodom and he understands that these people have no interest in his daughters. Lot's offer is meant to be offensive and indeed the people of the town immediately recognize that they are being criticized - "This one fellow came in to sojourn and he will need play the judge [he's judging us]?" This attack by Lot on standard immigration procedure in Sodom makes him the target of their rage in the same way the illegal aliens were the target just a few verses earlier: "now will we deal worse with thee, than with them."
Why the sin of Sodom matters:
The sin of Sodom matters because the Later Prophets regularly compare the nation of Israel to Sodom (Isaiah 1:9-10, 3:9, Jeremiah 23:14, Ezekiel 16:41-56 and more.). If the sin of Sodom was sodomy than this comparison seems hyperbolic and inconsistent with all the common themes in the Later Prophets. However, if the sin of Sodom was xenophobia, insularity and a lack of social justice then this criticism is perfectly consistent with the messages that permeate the prophetic writings from that time.
Lot had no intention of giving his daughters over to people of Sodom and their original request to Lot had nothing to with sex. There was no sodomy in Sodom.