A lot of folks would not agree with me, but I would like my horse to back primarily from the rein. I do, however, change my body attitude and will very lightly brush my leg against the side if the horse needs further clairification.
If you pull backward on both reins and the horse only resists this pressure as much as he can, then when he feels he has nowhere to go he goes UP, then you need to break it down and break him out.
Break it down means bread the process down into more comprehensible to the horse. Like, rein on means give your jaw to the bit :rider reward . Rein on means give your jaw and your poll; rider reward/release. Like that.
Break him OUT means that when he is giving to the bit, but just coming back behind it and getting kind of "stuck", like he doesn't know where to go from there, or his mind is turning back toward stiffening against your rein, then pick up one rein much stronger than the other, bend him back and get him to step back and under with his inside leg. Drop all reins;reward! Ask for a back, he freezes, pick up one rein and address his inside HIND leg, he bends and steps under/back, you release and try again.
Soon, all you have to do is ask for a back with one rien slightly tighter than the other to create a little bend so that he doesn't brace agains the equal pull, when he bend and steps back, then you kind of switch the "back" signal to the other hand, he should change his bend a tiny bit and step back on that side.
It's the old trick of bending a horse out of a brace. Alternate sides when you do the bend/ask for back up. You may need to creat a lot of bend and even brush his inside flank with your foot to get him to step the inside leg over.
eventually he will not need to step under/over (break out) but will back straight up with a soft jaw.