I once watched a recently graduated, successful 4-Her give a county-wide demo to prospective young 4-Hers on how to show a horse. The whole time she was trying to talk, her horse was pushing into her and making her move her feet for him. She just smiled and rolled her eyes. I thought, "I don't care how successful they were in the show ring; that horse has no respect for his owner."
This pushy lack of respect can become dangerous, especially in situations where a horse is nervous or frightened. There are numerous videos on You Tube of horses literally knocking their owner's to the ground and trampling them. This is partly due to the horse's herd instinct. A horse knows instinctively that the safest place for them in the herd is at the center. A frightened horse will thus push to the center of the herd. That instinct doesn't disappear even if the "herd" only consists of a horse and it's owner.
Horses are always testing herd leadership. A test may be something as simple as a horse nosing at you or pushing her shoulder toward you while keeping her feet still. The horse has invaded your personal space and you automatically step backward without thinking about it. The next time, she might push her shoulder toward you and casually take a step toward you. You, of course, don't want to get stepped on, so you step back again. A pattern has begun to develop and the horse thinks she must be the leader.
Learn to read the horse's body language. If the horse even starts to shift his weight toward you without you inviting him in, gently but firmly ask him to shift back or to take a step away from you. Teach your horse to back up just by wiggling your rope. Once he has learned this, you can ask him to back no matter where you are standing in relation to your horse and you never have to move your feet to do so.
If I am standing to the side of a horse and she pushes toward me, oftentimes I will ask her to yield her forequarters away from me. Do this every time the horse pushes into you and it won't take long before the pushy behavior is extinguished.
Make sure to use phases of firmness (I count to four for each phase and then increase pressure as needed) and continue asking until he complies. Remember, your horse learns what to do or not do from the release of pressure. If you quit asking before the horse yields to your request, you have just taught him to ignore you.