your instructor is telling you to set your hands agains the horse in hopes that the horse, getting no release from leaning on your hands, will choose to come off the pressure. This works. But, you have to be very good at rewarding the horse's attempts to come off the bit, so you have to have a ready feel for when he gives , even the tiniest amount, and reward the horse's "give" with an even bigger "give" of your own.
Also, you cannot just meet his pressure in exactly the same mount. you meet his pull, but you add just one ounce more. you donn't want to equal him exactly because you are only giving him as much resistance as he is willing to put in, so there is no reason for him to give to you. you are stuck in a stalemate. By adding the tiniest bit more, the hrose is given a reason to reconsider his habit of leaning on the rein and to try something different, such as giving to the bit.
However, if you don't see his "try", and you don't reward him for it, he will simply up his resistance to match yours. Do you get it?