I would argue that the typical person meets a horizontal force with another horizontal force in the same direction, typically by using their arms and shoulder, or maybe if they're "good", using their hips and relaxed arms to push along the same horizontal direction.

Someone with skill isn't going to push along the same direction (a vector is really the proper term). Pushing "upwards" or vertically works well to to deal with an incoming force, but you don't really push upwards with your arms, or legs (or anything) as in that case you are actively pushing against the incoming force.

You would have to figure out how to take the horizontal force within you and convert it into a vertical force that goes down into the ground and then goes upwards

Mike Sigman's ground path exercises are a foot in the door for this stuff, since they initially teach you to relax and not try and add anything to push back. You do have to transition though, as the initial bringing it to the back foot seems to allow you to "push back" with the pushers force, but along the same direction. You have to figure out how to convert that push to a vertical component, as the more "vertical" the component, the harder it is for the pusher to exert force on you as they have nothing to push back with.

Strangely, the more vertical your reflection of the push from your partner is, the less you feel your partner and the less they feel you too..........