My daughter is going thru similar issues. We already have several meatless days each week, but she's pushing for no meat. Or chicken. Or eggs, because they could have become chickens.
In her brain, it means she should get cheesy pasta or grilled cheese sandwiches every night. That's not okay with me.
I told her we can cut meat out entirely when she starts eating various legume dishes, and broadens her spectrum of vegetables beyond the standards. Sure, I'm fortunate there's never a fight about eating broccoli, cauliflower or asparagus - but she won't eat eggplant, squash, spinach, etc., or any fruit that's not an apple, grape or banana.
She's trying more of the "grown up" vegetarian dishes now, and there's less fighting at the table about eating cute & fuzzy creatures.