How do you grip the pull-up bar? If you say with all five fingers over the bar (like a monkey grip) then you need to change. To ensure the right grip, reduce the risk of tearing, and stay safe, you should grip the bar with your pinky knuckle over the bar and your thumb wrapped around the bar, not on top. Also, grip the bar across the middle of your palm, not where your fingers meet the palm. It’s the same way you’d grip a barbell.
This is, by and far, the stronger grip. It can keep your shoulder more stable, reduce the risk of tearing, and, hopefully, keep you from slipping off the bar. It also helps build grip strength and works to activate your lats.
Have a weak grip? Active bar hangs and farmers’ carries can strengthen your grip.