You should coax him into it instead of going straight up to him. Offer him treats and slowly get closer as he takes them. Don't go straight for the face, aim for scratching the neck or withers. Also some exercises to build trust is lunge him on a lunge line and before you switch sides or finish, make him come to you. You can do this by lightly pulling on the line to make him come, then make him follow you. Once you have this down, try free lunging. This is no lunge line. Make him come to you. Don't give up until he does and don't give in and go to him. It is frustrating and may take up to an hour or more but don't GIVE UP once you start. It will pay off I promise, I had to do this with an abused horse at the stable where I train. And when you do get to pet him give him treats as a reward for letting you.
This is pretty advanced ground work that shows dominance, and I don't know if you're up for it, find someone to help you, but in the end the horse must know you're boss
Oh my word.. I have no idea if I agree with any of this with a horse that is already acting pushy and NOT frightened. Pushy =/= give treats or free lunge. That is giving you doormat status instead of leader status.
If I did that with my pushy horse, he'd get WORSE not better.
This isn't an abused horse, and this isn't a frightened horse. This is a horse that wants someone to look up to to PROTECT them from predators (aka a herd leader)
You shouldn't even do this with an abused horse. Free lunging is not safe when you haven't established trust and respect. You're asking to be attacked and for them to feel like they are trapped and are unsafe.
OP please don't do the above. That's going to make things worse.
You must think like a horse. Horses don't go around giving each other treats and go up to a random horse without laying down the ground rules and sticking up for themselves. That would get them seriously beat up (think lowest horse in the pecking order)
You need to have space. If this horse pushes into your space, you push him out. If he kicks out at you, you take a crop and get after him for it like you mean it.
What he wants to know is if HE were a predator, would you stick up and protect him from it or would you curl up into a ball and run away screaming and let them eat you? He's hoping for the first option as that is going to keep him alive. And that would be in his best interest to follow that leader.
So you need your space. Once you have your space, then on YOUR terms you can allow them into your space, as they can allow you into their space (and they will once you show you're a leader)
And I don't mean smacking the horse every time he blinks. That doesn't TEACH him anything. Teach him you need space, he stays out. Teach him he is NOT allowed to bite or kick out at you. Praise him when he does something REALLY good, otherwise leave him alone. Give him scratches behind his ears and on his neck every now and then.
You are a leader, you are a teacher (not a trainer..) and you need to let him know you can step up and protect him by correcting his naughty behavior and enforcing his good behavior.
Does that help?