When I was a kid, my family had a scary experience at Walt Disney World. We were riding in the cable car that went over the park. There was a turn in the course, and the car was supposed to release from one cable and hook onto another at this turn. For some reason, our car didn't make the hookup, and we were stuck at the turn until the next car came along and hit us. They stopped the ride, and we sat there for what felt like forever while the crew sorted things out and determined that we were safe to continue the ride. Don't remember that I had a problem with heights before then, but I sure do now!
The thing about not letting a horse move you is relative, of course. I mean, you aren't supposed to just stand there and take two feet in the face; dominant horses dodge that sort of thing, too.The point is that you aren't letting the horse push you around. You may move to dodge, or block, or whatever keeps you safe, but you don't retreat. That's the difference.
Behaviorists use the term extinction when they talk about trying to get rid of a certain behavior. Whether the subject is human or animal, they do what they do because in some way, they get a reward for doing it. "I do this, and this other thing that I like happens." The trick is to short-circuit that behavior-reward cycle.
Latte used to take shots at me with her face while I was leading her - deliberately smacking my face with hers. Knocking me around was her way of showing that she was higher in the pecking order than me. I learned to watch for the move, and get my hand up to block (so she'd hit my knobby knuckles - ouch for her!) or give a sharp jerk on the halter (also ouch) before she could get to my face. The reward (making me move) wasn't happening, instead, something she didn't like happened. When I picked out her feet, she'd do these little experimental kicks or almost -touch-me nips ( "testing, testing . . . .1 . . .2 . . .3 . . . 4.") I couldn't ignore any of that mess; I learned to watch for it and head it off while she was still in the "thinking about being bad" stage. The problem with getting rid of bad behavior, is that you can't ever let the reward happen, or you go back to square one. Also, in the early stages of extinction, the bad behavior usually escalates - it's like pushing the button again and again, trying to get the positive thing to happen, before it finally sinks in that it isn't going to happen, so there's no reward anymore.
Eli bites - why? What does he get out of it? Is he just expressing frustration, is he trying to get you out of his space, is this play for him; what reward does he get for this? He's way, way, wa-a-a-y more than old enough to know better than to bite people; I'm betting that at some point he did know better, but has returned to this behavior because he gets something out of it. Obviously, he can't bite you if he can't reach you, so stopping the biting involves making sure he only comes into your space at your invitation, and controlling him when he's in that space. You need to be aware enough of what he's doing that you can block any bite attempts before they happen, and that means reading his body language well enough to know when he's thinking about it and being prepared to block/redirect before he tries. If he's acting antsy and dominant, you move him. He only comes into your space when he is acting appropriately. If he slips past your guard and manages to score a hit, you need to get on his case immediately - yell, smack him, back him up, whatever; he needs to understand that that kind of thing gets him stuff he doesn't like now. Minis are smart; he won't keep pushing a button that has a negative reward (though he might experiment in that direction every once in a while to find out if the rules are still the rules - horses do that).