Well first, you have to look at the equipment you're using. What brand of rasp did you go for? If you go for a cheap one($12-15 bucks) that thing couldn't even rasp paper! I found a rasp on sale, tried it out, and it would NOT rasp the foot. So that was a waste of money. You need a good quality brand hoof rasp which will cost you about $25 bucks.
For my boys, I usually trim them with their hoof on my knee. I hold their hoof in place with my inner arm so I can nip with both hands. Then I stand and hold their hoof with my inner hand and rasp with my outer hand. Then I switch hands to make sure I rasp the inside just as well. You may also be pressing too hard, or thinking about it too much. Take the fine side and go over lightly, first. That will help smooth things down and not give something for the coarse side to catch on(this was a handy tip my farrier taught me after he saw me catching on the horse's toe). So if you get caught up on something with the coarse side, ease up on the pressure and use the fine side to smooth things out a bit. And just because you can't rasp in one direction, doesn't mean you can't rasp another. If your rasp just won't stop catching going one direction, flip the rasp around and try going the other direction.
Side note: It is mandatory to draw blood. At least a dozen times. Last time my farrier watched me trim, I caught my thumb knuckle and kept going without saying anything. My farrier saw, asked if that was blood, and when I said yes, he said "Good!"