Question

Does Entrainment cause your opponent to have your ability or you to have your opponent's ability?

Answer 1

"It dances a mysterious rhythm. It makes the opponent copy & makes both of their abilities the same."

It makes your opponent have the same ability as you. But these are the only pokemon that can learn it so far:

Plusle (Plus)
Minun (Minus)
Buneary (Run Away/Klutz/Limber)
Lopunny (Cute Charm/Klutz/Limber)
Chingling (Levitate)
-Chimecho (Levitate)
Tabunne (Healing Heart/Regeneration/Klutz
Hahakurimo (Swarm/Chlorophyll/Dust Proof)
Churine (Chlorophyll/Own Tempo/Leaf Guard)
-Doredia (Chlorophyll/Own Tempo/Leaf Guard)
Aianto (Swarm/Hustle/Truant)

using it with Aianto sounds pretty promising if it has truant though. You could Give your opponent's entire team Truant just to be a jerk. But I'm not sure if it's like skill swap or synchronize in that its effect still applies after your opponent switches.

Comments

I'm guessing there will be exceptions, and Truant will be one of those exceptions.

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My thoughts exactly, which is why I skipped the Aianto moveset.

Answer 2

It makes the opponent have your ability.