The Genesis passage most certainly does not clearly explain that it had anything to do with homosexuality. Sodom had already been deemed worthy of destruction before the Angels were sent to rescue Lot and his family, and see if they could find enough righteous me to spare the city based on Abraham's request. The fact that the men of the city tried to rape the angels does not mean that homosexuality was the sin that condemned them. Even if their attempted rap (which I as I said happened after the city was already scheduled to be destroyed) was the reason for the destruction, gang rape is something very different from consentual sexual relationships. The special seriousness of the sin may have been based on the fact that the were angels, rather than the fact that they appeared male. Perhaps more importantly, it could have been base don the fact that the were guests. It is important to note that none of Jesus's four references to he Sodom and Gomorrah in the gospels mentions anything sexual. Three of the four explicitly tie their judgement to their failure to welcome strangers. Customs of hospitality was a very big deal in ancient cultures.
The association between the Sin of Sodom and homosexuality did not arise until the middle ages. Jewish sources related it to their treatment of the poor and of foreigners long before that.
Here is the passage in question.
Genesis 19:1-25 And there came two angels to Sodom at even; and Lot sat in the gate of Sodom: and Lot seeing them rose up to meet them; and he bowed himself with his face toward the ground;
2 And he said, Behold now, my lords, turn in, I pray you, into your servant's house, and tarry all night, and wash your feet, and ye shall rise up early, and go on your ways. And they said, Nay; but we will abide in the street all night.
3 And he pressed upon them greatly; and they turned in unto him, and entered into his house; and he made them a feast, and did bake unleavened bread, and they did eat.
4 But before they lay down, the men of the city, even the men of Sodom, compassed the house round, both old and young, all the people from every quarter:
5 And they called unto Lot, and said unto him, Where are the men which came in to thee this night? bring them out unto us, that we may know them.
6 And Lot went out at the door unto them, and shut the door after him,
7 And said, I pray you, brethren, do not so wickedly.
8 Behold now, I have two daughters which 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: only unto these men do nothing; for therefore came they under the shadow of my roof.
9 And they said, Stand back. And they said again, This one fellow came in to sojourn, and he will needs be a judge: now will we deal worse with thee, than with them. And they pressed sore upon the man, even Lot, and came near to break the door.
10 But the men put forth their hand, and pulled Lot into the house to them, and shut to the door.
11 And they smote the men that were at the door of the house with blindness, both small and great: so that they wearied themselves to find the door.
12 And the men said unto Lot, Hast thou here any besides? son in law, and thy sons, and thy daughters, and whatsoever thou hast in the city, bring them out of this place:
13 For we will destroy this place, because the cry of them is waxen great before the face of the Lord; and the Lord hath sent us to destroy it.
14 And Lot went out, and spake unto his sons in law, which married his daughters, and said, Up, get you out of this place; for the Lord will destroy this city. But he seemed as one that mocked unto his sons in law.
15 And when the morning arose, then the angels hastened Lot, saying, Arise, take thy wife, and thy two daughters, which are here; lest thou be consumed in the iniquity of the city.
16 And while he lingered, the men laid hold upon his hand, and upon the hand of his wife, and upon the hand of his two daughters; the Lord being merciful unto him: and they brought him forth, and set him without the city.
17 And it came to pass, when they had brought them forth abroad, that he said, Escape for thy life; look not behind thee, neither stay thou in all the plain; escape to the mountain, lest thou be consumed.
18 And Lot said unto them, Oh, not so, my Lord:
19 Behold now, thy servant hath found grace in thy sight, and thou hast magnified thy mercy, which thou hast shewed unto me in saving my life; and I cannot escape to the mountain, lest some evil take me, and I die:
20 Behold now, this city is near to flee unto, and it is a little one: Oh, let me escape thither, (is it not a little one?) and my soul shall live.
21 And he said unto him, See, I have accepted thee concerning this thing also, that I will not overthrow this city, for the which thou hast spoken.
22 Haste thee, escape thither; for I cannot do anything till thou be come thither. Therefore the name of the city was called Zoar.
23 The sun was risen upon the earth when Lot entered into Zoar.
24 Then the Lord rained upon Sodom and upon Gomorrah brimstone and fire from the Lord out of heaven;
25 And he overthrew those cities, and all the plain, and all the inhabitants of the cities, and that which grew upon the ground.
The bit in bold clearly shows that they wanted to have sex with them. There are two terms used in the Bible to describe sexual activity, one "to uncover their nakedness" and the other is "to know". In Genesis 5 we see that "Adam knew his wife and she conceived" Showing how they use the term for sexual activity. The fact that Lot offered his daughters instead of the men that turned up showed that their desire was sexual activity an the men of Sodom had the gall to complain about how Lot was judging them. We have a similar situation in the book of Judges.
Judges 19:22-30
Now as they were making their hearts merry, behold, the men of the city, certain sons of Belial, beset the house round about, and beat at the door, and spake to the master of the house, the old man, saying, Bring forth the man that came into thine house, that we may know him.
23 And the man, the master of the house, went out unto them, and said unto them, Nay, my brethren, nay, I pray you, do not so wickedly; seeing that this man is come into mine house, do not this folly.
24 Behold, here is my daughter a maiden, and his concubine; them I will bring out now, and humble ye them, and do with them what seemeth good unto you: but unto this man do not so vile a thing.
25 But the men would not hearken to him: so the man took his concubine, and brought her forth unto them; and they knew her, and abused her all the night until the morning: and when the day began to spring, they let her go.
26 Then came the woman in the dawning of the day, and fell down at the door of the man's house where her lord was, till it was light.
27 And her lord rose up in the morning, and opened the doors of the house, and went out to go his way: and, behold, the woman his concubine was fallen down at the door of the house, and her hands were upon the threshold.
28 And he said unto her, Up, and let us be going. But none answered. Then the man took her up upon an ass, and the man rose up, and gat him unto his place.
29 And when he was come into his house, he took a knife, and laid hold on his concubine, and divided her, together with her bones, into twelve pieces, and sent her into all the coasts of Israel.
30 And it was so, that all that saw it said, There was no such deed done nor seen from the day that the children of Israel came up out of the land of Egypt unto this day: consider of it, take advice, and speak your minds.
In this situation again these men of Belial wanted to have sex with a man who had come into a house, but this time instead of not stopping and doing the women like in Sodom, they raped the woman basically until they all had their way with her. The only difference between the two situations is that the men of Sodom would not stop until they got what they wanted, which was sexual activity with the men until they were blinded by the angels, and the fact that the men of Belial did allow themselves to fulfil their sexual wants with a woman. If you read chapter 20 of Judges you see that the rest of the nation went to war against the tribe of Benjamin, where this took place and eventually punished those who were responsible. Both of these passages show what happens when sexual lust get control of a group of people and how God deals with, by punishing those who commit such sins against God.