I have always been confused when it comes to cutting avatars with this exaggerated hairstyle, any suggestions?

Fit as much of the hair in the cut as you can. It's the only case in which it's allowed to include more than 2-3 pixels beneath and above the head.

I also urge you to crop the source image to an area around the face before putting it through remove.bg. Not doing so will cause the eventual cut to lose sharpness - compare the approved cut with yours for an example.