I can see the confusion. In most cases, "move against" means to oppose something, or even attack something, for example:
Syrian troops moved against rebel strongholds in the city of Aleppo.
We should quickly move against the enemy's advance through this valley.
Since the Convention was drawn up international opinion has begun to move against it.
When describing tectonic plates, however, the authors wanted to say something akin to "rub against". As with many English phrases, the challenge is to use a verb that conveys the right image. Rub implies a gentle motion, like a cat against your leg. "Grind against" might work, like a car wheel scraping along a curb, but for whatever reason the authors chose the generic "move against", despite its alternate meanings.