AITA for letting my ex keep my dog?

I(25f) recently broke up with my ex (27m).

We were together for 5 years and have had a dog in common for all of our relationship. The last two years have been a living hell and finally, after a lot of therapy, I realized the relationship was abusive and finally left him for good.

We’ve been on and off for the last 6 months and had agreed to each have the dog for a month. Since I decided to end the relationship for good, he is threatening to keep the dog from me and not letting me see him ever again, he said he got him for me and so, he can easily take him away.

Now, would I be the asshole if I let him keep the dog? I love that baby with my whole heart, but I know my ex is using him as leverage against me, and I don’t know if I can take the back and forth forever. What would you do?