If he reacts to the cinch that might also be part of why he does it when you groom him.
The cinching issue is most likely due to the one who started him not giving the horse enough time and confidence when introducing the saddle.
To help with that cinch slowly and pet her belly under the cinch while you do it. She will still react and it will take time. Also tighten the cinch quite a bit but without locking it in just hold it tight so that if you let go it comes loose. You tighten and she will try and nip and bite. Don't punish her just hold the tightness. When she stops you let go of the cinch and let it loose and pet her. And repeat. As soon as she calms down you let go. She will react less and less.
Also have her walk a few steps once she has calmed down and you have let go of the cinch. Like 3 or 4 steps and then stroke and repeat. The steps will also make her feel less trapped which is what the cinch causes her to feel.
For brushing try and do it not when you ride or excercise. Like when you graze her bring a brush with you and stroke her with it. Also try and not tie her or not do it in her stall. Hold the rope but don't tie her on the walls.
This will make her feel less trapped and increase the chances of her
Always let her smell the brush before using it. And if she wants to move forward let her. Stop her if she is trying to go away but otherwise give her some freedom of movement.
It will take time but it will improve.
Neck, back and belly, ...usually mainly before we exercise/saddle...not after. Generally a sweet horse, not really pushy, except when there are treats, so I avoid those
I do but first please answer these:
Is he especially annoyed when you groom him on his belly or any other part?
Does he do it also when you saddle him?
Is he pushy in general?
For now know that punishing is always wrong. Because it implies no real understanding of his behaviour.