First thing is to take a step back and think logically. Sometimes, we're made to feel accountable for our moral beliefs and those of Islam's. We become worried about appeasing the feelings of those who don't understand and making sure that our remarks are "politically correct". In doing so, we run the risk of providing inaccurate information.
Second thing, deconstruct their question bit by bit. "If your religion is about peace, equality, and all of that how come it is against someone being homosexual then?"
Okay well, let's see. Islam isn't the only religion that's against homosexuality. The other two monotheistic and Abrahamic religions are as well. And they are believed to be peaceful as well. The same question applies to them. In the case of Islam, it's against homosexuality because God created males and females for one another. It is the natural order of things. It is the way he designed humanity. There's a literal basis to the phrase, "It's Adam and Eve, not Adam and Steve." When homosexuality comes into the picture, God's original design is being challenged and distorted. It disrupts the natural balance of things you see. Look at nature. Your basic mammals and primates don't mate with the same sex. It is God's natural design and homosexuality goes against nature. Engaging in homosexual activity also leads to harmful side effects such as an increased risk of HIV/AIDS and anything that emphasizes a harmful lifestyle in Islam is forbidden because we are not supposed to engage in behavior that is detrimental to our health and our well-being.
This logic has nothing to do with peace and equality. Man has chosen to alter the Laws of God and create an unnatural lifestyle. As Muslims, we live our lives the best way we can and leave others to their whims because we are not responsible for them. Yes, we do dawah and educate them the best way we can but in the end, we cannot force them to live a certain way. It's their decision in the end. We may not have the right to hurt them but that doesn't mean we have to agree with their choices.
People need to understand that. Everyone has their own sets of morals and beliefs. Just because the current trend is to "go gay" and be all accepting and warm towards them doesn't mean that everyone will automatically follow what's trendy. We stand by our beliefs and as long as we're not hurting anyone, we have every right to do so. Just like these people have their right to hate Muslims and Islam, we have our right to hate homosexuality. As long as no one acts on it and rights aren't being violated, I fail to see the problem.
Bottom answer: God's Law is to preserve the natural order of things. That's why we're against it. Because we don't promote challenging His Laws. Why? Because He is Our Creator and He loves us. We in turn love Him for all of His Blessings upon us and we strive to please Him by obeying His Commands. And that is by not challenging what He has created to be natural.
And we're back full circle.
For us, we have to go beyond saying something is simply HARAM and forbidden. I'm sorry but that does nothing for many people and it certainly does nothing to sway hearts and minds. Unless you're already in the fold of Islam and willing to follow the rules, it doesn't do much to tell people something's forbidden. If anything it increases their rebellion.