For a HS student, the assignment seems like great work. The arguments are a bit flawed if you think about them, but agreed that OP understood the premise. I outlined a few potential counter-arguements below if you want to beef up your assignment in the future. Also, your last points about classifying legitigate accusations of wrong doing or hate speech as "gossip" negates some of your points about the benefits of "gossip." I think you should also be clear about how you define "gossip".
Gossip doesn't act as a "warning" because there is no verification if what is being said is true or the motives of the messenger. It can be a deterent, though.
The LBGT example would be more aligned with hate speech and spewing hateful rhetoric opposed to "gossip".
Bonding? Sure. But, I'm not sure I would equate gossip with venting.
I'm also not sure I would call gossip a gendered term, at least not in my culture (I'm nor in the US.) It is seen as a derrogitory term, sure, but this one can be up for interpretation.
Gossip being aligned with supression can also be argued away. If it is a factural point that can be proven, would you classify it as gossip?