God does give a partial reason for why he don't want it, as the verse state it is considered an abomination, but also it makes people "unclean". Apparently those before the Jews did it and God doesn't like that.
Leviticus 20:13
13 - If a man lies with a male as with a woman, both of them have committed an abomination; they shall surely be put to death; their blood is upon them.
Leviticus 18:22-30
22 - You shall not lie with a male as with a woman; it is an abomination.
23 - And you shall not lie with any animal and so make yourself unclean with it, neither shall any woman give herself to an animal to lie with it: it is perversion.
24 - “Do not make yourselves unclean by any of these things, for by all these the nations I am driving out before you have become unclean,
25 - and the land became unclean, so that I punished its iniquity, and the land vomited out its inhabitants.
26 - But you shall keep my statutes and my rules and do none of these abominations, either the native or the stranger who sojourns among you
27 - (for the people of the land, who were before you, did all of these abominations, so that the land became unclean),
28 - lest the land vomit you out when you make it unclean, as it vomited out the nation that was before you.
29 - For everyone who does any of these abominations, the persons who do them shall be cut off from among their people.
30 - So keep my charge never to practice any of these abominable customs that were practiced before you, and never to make yourselves unclean by them: I am the LORD your God.”
The interesting things is that God changed his view on how this should be punished in just a couple of pages, slightly confusing
. First they should just be cut off from their people, two pages later they shall be put to death.
Why God would allow homosexuality's to exist in the first place is a good question. There doesn't seem to be any beneficial reasons for it to exists, just as there doesn't seem to be any downside to it either.
From what I can see from some of the replies you have gotten, some talk about free will, you yourself mention sacrifice, I have heard other explanations that it is a test, which I guess is sort of like what you mean by sacrificing as well? But personally I don't think any of these explanations make any sense.
In regards to free will, I don't see what this has to do with it at all. And even if it were the case, God ought to let people act on it as they please, otherwise what is the point for free will, if you should get killed for it and God explicitly say that it is their own fault. Which could be another way of saying that God is not going to look at this lightly.
Sacrificing/test as you mentioned, I don't buy either, at least not if we are talking about a just God, why is it that certain people should have to sacrifice in regards to this, when others doesn't have to? Also this idea falls apart I think, the moment we look at the animal kingdom. Because a lot of other species do homosexual acts as well, but I think it is a bit of a longshot trying to justify that God is also testing or demanding sacrifice from these animals, who clearly doesn't seem to care at all. So why would God allow or make it possible for animals to be homosexuals', that doesn't seem to make a whole lot of sense.
Personally I think this is linked to the role of man and women. The bible puts men above women and as the head of the family, basically being able to do what they want. Like selling their daughters etc. so for men to take the "role" of a women, I think would have been seen as a step down the ladder in regards to this hierarchy. At least I think that is the most obvious explanation, when taking into account the time, history and how the bible in general speak about the different genders.