The key to climbing ropes is using your legs in conjunction with your arms (unless by "climb a rope," they mean solely using arm strength). My mother was a tremendous rope climber when she was younger, and she always said you must use your legs.
Otherwise though, it is just upper-body strength in regards to doing pullups, primarily in the upper back (lat muscles). If you can't do one pullup, go to a pulldown machine and start doing pulldowns. Work yourself up to pulling down your own weight, then go start cranking out pullups. Just don't throw your lower back into the pulldowns; use solely your upper back muscles.
Try following the Armstrong pullup program (google it), only in your case do pulldowns.
Women are naturally physically weaker than men are, but they are still plenty caable of getting the strength and endurance to manage 20 pullups, they just may have to work harder is all.