Dont use a dressage whip i saw someone at a show once walking their horse and he spooked when a rider walked past with one and flipped himself over from rearing. Make sure he isnt paying attention to something else or looking away from you as that causes his shoulder to fall into you. So always make sure he is listening to you, and if your having a hard time achieveing this try join up. After youve gotten him to listen and pay attention to where your at if he still steps on you then hold farther down the lead and walk farther from him and when he steps into you, take a step towards him and make him back or swing the rope at his chest until you can step back and he doesnt follow you until you ask him to follow you
Start with the oldest one from me... I didn't realize they'd go in this order lol
Also, just make sure that once you do it once, you always lead from near the end of the rope
Anyway, what you need to do is hold the lead rope near the end, whereas most people lead from right beneath where the lead rope attaches to the halter. Walk a few steps and then turn towards your horse, stopping. If they don't stop, swing the lead rope back softly three times. If they don't move back do it a little harder for three times, then a little harder, and so on until they move. When they go back a step of two, make sure you reward them by rubbing their forehead. Do this over and over until he almost gets to the point where he leans back when you turn towards him instead of continuing to walk.
What some of these people are telling you is completely wrong. Do NOT use a whip if any kind. You teach your horse to be afraid of the whip and run from the whip which ended terribly for me at a show once when a someone was lunging their horse and using a whip (which you also should not do) and the crack spooked my horse. Let's just say I ended up with a broken arm and sprained ankle.
My horse had no respect in the beginning, and I tried liberty not long ago! I bought a dressage whip and worked on basic tricks (like backing up by pointing my finger, and having him stop when I stop so he isn't leading me) I took him in a round pen and tried tapping the front of his legs while clicking and pushing him back. The treats were there to tell him when he was right, and little improvement came a long way! Now he doesn't need a halter (but I do use one) and pays attention! He is out of my way and is respectful!
I would recommend using your hands and pushing with spiky fingers first, but if that doesn't work, I would bring a dressage whip and carry it in the hand holding the lead rope so that it is in between you and the horse. Then, when he is impolite or flat out rude, flick your wrist so it taps him on the haunch. It is a touch harsh, but it helps.
When he gets too close to you, push the pressure point above his shoulder to get his to move over then release when he takes a step away. Keep doing this every time he gets too close and eventually he will learn to walk a step away from you.