What martial arts rely on using the other person's attack against them?

I took some Aikido lessons. It is purely reactive. You can’t use Aikido to attack someone. I am not familiar with Judo, but I thought it was similar in that regard.

You are practically defining “Judo”. The Gentle way.

Hapkido and as @LostInParadise mentioned Aikido are both styles that use the opponent’s moves against them.

Aikido is mostly purely defensive, and the philosophy of the art is to be fluid like water, and use your opponent’s rhythm against them. So for example if you were attacked with a punch, a defense would be to sidestep, grab your opponent’s punching arm with one hand and put your hands on the back of their shoulder with the other—swing them around you using the momentum of their attack and to throw them off balance and then use the shoulder placed hand to force them to the floor face down. From there you can either back off, or twist their arm into submission.

Basic aikido starts at teaching you how to break locks, basic defensive moves, rolling, and Ukemi (breaking falls), and you would be falling plenty in Aikido so learning how to break your fall is an essential technique.

Here’s a youtube video that gives a nice look into Aikido.

Thanks folks. Do you know any good websites that are reliable about how good different schools are? I’m looking for something in Brooklyn.

So, in aikido, it is not exactly against the opponent, it is uniting with him. Which is the best solution in longer terms. Other one is, as mentioned, judo/jujitsu.

@roundsquare If you are interested, Spike Spiegel does Jeet Kune Do. It is not a fictional martial art, but rather Bruce Lee’s method of fighting. I recommend learning another martial art before trying JKD, though. Any of those mentioned above will do. Lee started with Wing Chun, of course, but that is not at all necessary.

Tai Chi is totally that.
In the core principles it has ideas like ”四倆拨千斤” (4 grams can move a 1000 kg) or ”以柔制岡” (to use the soft to subdue the hard). You just need to find a sifu who teaches push hands…