The aliens in Arrival make contact with the humans and try to get them to learn the their language because it's important that the humans learn the alien language, not the other way around.
By grasping the alien language and thus the thought processes necessary to understand it, the main character Louise
gains the ability to see past and future events (as the aliens do) and thus avert the attack on the alien ships by the Russians, Chinese and others.
Also, the aliens reveal
that the reason they do this is that in the far future (from the human linear perspective) they will need help from humans.
So, the aliens are not "playing dumb" about understanding human language. Maybe they do understand human language, maybe they don't. From their perspective it's irrelevant because they need the humans to understand their language in order for humans to gain the new perspective on past and future time.
Presumably just coming out and saying "hey x in your language means y in our language" would not let the humans make the necessary mental leaps for them to change their perception of time.