"Oh, so that's it? I'm only useful if I have magic? That's all that matters?" There was a lot of that Emma hadn't unpacked yet, her place in the world being what it was. Her value was constantly attached to being the savior, being Snow and Charming's daughter, having magic. That was what she was to all those people; something created from True Love, a power source.
She wasn't Emma Swan, friend and family member, she was the Savior, Snow and Charming's daughter Emma. And sometimes that was too much for her, she just wanted to be Emma, just wanted to know that people wanted her for her. Not because of what she could do for them.
"Forget the fact that I've proven I can take care of myself without magic, that I can fight and lead, and contribute without having sparkly powers." Because who wanted to think that all they were around for was because of weird powers they had because mom and dad loved each other. "So if being me, without magic, is wasting anyone's time, feel free to lock the door behind you, because I'm sorry I'm not what you want."
But she could deal with that, because she was used to that, so screw them. If they couldn't just accept she didn't have that anymore, she wasn't what they wanted so badly, and pushing it on her wasn't going to change anything.