My GCC is a big fan of fruit, but I've been working on getting her to eat veggies. She's extremely suspicious of new foods, and it's been pretty tricky.
Unless I'm giving her something she knows she loves, she's less likely of eating something if it isn't cut into tiny pieces. Also I've found it helpful to eat a piece myself and show her that it's food, it's delicious, and it's safe.
Sometime's she'll reject things, but come back to them later for weird reasons or no reason at all. Like, I figured out that she doesn't like warm foods, so anything I cook for her needs to be refrigerated before she'll actually eat it. Sweet potatoes she didn't want to try at all (I think because of how soft they are), but eventually she changed her mind for no apparent reason and now she loves them.
The best advice I keep hearing is to be patient and keep trying.
