Some good stuff here. Lateral work needs forward movement when first teaching it to a horse that doesn't have a clue. it's much easier to have the forward movement, THEN use your leg to cue the horse through "the open door". You can't just ask a horse that HAS no clue, to move away from the pressure laterally from a standstill. The lightbulb does NOT go on, and yep...they will usually back up because they KNOW how to do that at this point in their training.
I had an AQHA gelding that took over 6 months to teach lateral, then side pass. He was simply on the lower end of the learning curve. So any training was done when moving FORWARD. Like trotting into a corner, I would ask for a leg yield with a firmer outside leg...even if it was just for one or two steps of lateral. Then I built upon that consistently through repitition here and there throughout schooling session....until one day, that light bulb came on! He understood what I wanted, and finally understood...the shutting one door, but opening another one for him to go through. I had this horse sidepassing squares etc...and could manipulate his body parts together AND independently in lateral movements at all 3 gaits pretty much, but it took a long time and I was patient and it ALL started with forward movement.