If that bothers you, stop reading.
Okay, so. You say that feeling an attraction to someone of the same gender is not a sin. But "choosing" to be happy, to live your life in a way that is true to you, to the very core, IS a sin. A right, by the way, that you have and hold dear.
Honestly, I think that's worse than just saying homosexuality is a sin. Because by asking a person - teen, tween, or otherwise - to DENY what you readily admit is NOT a choice - that being the person to which s/he is attracted - is to ask them to be a liar. And unhappy. And in eternal conflict.
Something with which you do not have to deal, because you are not gay. It's like asking me to deny the color of my skin, or my shoe size, or my height. Or asking you to marry and love a person of your same gender.
It's not who you are. In any way.
And THAT is why they are killing themselves.