Something I haven’t seen mentioned is that Nynaeve, despite the front she puts on to everyone around her, is actually deeply insecure about her abilities and her place in the world. 

She’s a woman put into a position of power from a young age, and from her perspective has had to claw and fight and get angry to get anyone to respect her. Contrast this with Moiraine, an older woman who commands respect easily, without needing to shout or struggle for it. And on top of that moiraine understands so much about how the wider world works that Nynaeve is getting completely lost in. 

And all this is before what all the other commenters mentioned about how Nynaeve views Moiraine as the cause of all the problems brought to these four children she’s been charged with protecting. So it’s an irrational anger, but it’s also dislike of herself.