It's not childish, Rito, it's true. TLS only gives consideration and merit to theories and ideas about Jessie that fit its preconcieved guidelines. Any that are nontraditional or unusual (such as her being one of the things Cloud could've been thinking about in the rain in Hollow because of her apparent loss or that an actual flashback to her time on stage would not have hurt the game) are immediately frowned upon, argued with, and shouted down. Anything that might give her potential for going beyond what TLS thinks she should be is immediately shot down.
TLS can prove otherwise by being open, welcoming, and supportive to any ideas concerning her no matter what they are and by not arguing with any of them. And by promoting discussion of Jessie at all. And by creating a best moments video for her to go along with the others - she was deliberately voted against so she wouldn't make it into the video or get one of her own, her chances purposely sabotaged. The only way TLS can prove otherwise is to create that video. Words don't mean anything. Only action does.
No one posts art of just her in the fanart forum - it's always the same characters over and over. TLS needs to change that to prove she's welcome here. And also, TLS needs to make sure she's discussed just as much as every other character and given the same amount of attention that they are. And Odysseus, to really prove you like her, go back to her avatar. Show everyone you're not afraid to do that and that you're not ashamed of her.