The problem lies in the position of your shoulders.

You can clearly see on both pictures that your right shoulder (left in the picture) is slightly higher and more opened up (as in your arm is rotated further out) than the left shoulder. This causes the rest of the body from that point on (so arms, elbows, hands) to act different from each other.

I wonder, do you do any shoulder work? And by shoulder work I don't mean your typical fitness exercises like shoulder pressing with dumbbells. I mean stretching the shoulders in multiple ways, doing scapular pull-ups, scapular push-ups and scapular dips. This is all very important to do if you want to do a proper pull-up. You need to strengthen the muscles that support the upper back while doing a pull-up.

EDIT: I've seen many answers about the back and those are correct in some way, but the problem lies earlier in the body/posture. The fact that there is imbalance in the back isn't the main problem here. That's what it looks like in my opinion anyway.

The problem lies in the position of your shoulders.

You can clearly see on both pictures that your right shoulder (left in the picture) is slightly higher and more opened up (as in your arm is rotated further out) than the left shoulder. This causes the rest of the body from that point on (so arms, elbows, hands) to act different from each other.

I wonder, do you do any shoulder work? And by shoulder work I don't mean your typical fitness exercises like shoulder pressing with dumbbells. I mean stretching the shoulders in multiple ways, doing scapular pull-ups, scapular push-ups and scapular dips. This is all very important to do if you want to do a proper pull-up. You need to strengthen the muscles that support the upper back while doing a pull-up.

EDIT: I've seen many answers about the back and those are correct in some way, but the problem lies earlier in the body/posture. The fact that there is imbalance in the hands isn't the main problem here. That's what it looks like in my opinion anyway.