It sounds like your core and legs are in very good shape, but pull-ups require really good shoulder and arm strength. Don’t fret, it’s common that our lower body is more muscularly developed than our upper body. Do you work out at a gym at all? If you are a member, maybe you could arrange to have one of the fitness instructors plan a regimen that would work on building up your arms, chest and shoulders a bit more.

I’m in the same boat. I can run a 5k, bike 80 miles, etc etc… but no pull-up. Ever. I’m focusing on upper-body strength, and working on push-ups. Not all the same muscles, but a lot of the same, and I can do them at home. Whereas I mostly just hang off the pull-up bar we have, so that’s not as useful right now. You can do it – just keep at it!