Sports generally reward bulk, speed, strength, and, often, height—all traits in which men tend to have the physical advantage. But climbers can’t rely on brute strength alone. The typically feminine assets of balance, flexibility, and a sprinkle of grace are essential to navigating the vagaries of ancient rock and plastic gym holds. (To effortlessly “dance up the wall” is a high compliment.) Excessive bulk, be it muscle or fat, while not a showstopper, is a definite disadvantage in a sport that rewards a high strength-to-weight ratio. Height can help or hinder, depending on the contours of the rock.I can attest to that from personal experience.
I once took a couple of people out rock climbing who had never been before, a man and a woman. All three of us were in the Navy and were in good shape. We were working on a climb that was relatively short (about 50 feet) and in the middle of the difficulty grades. The man was very strong, but like many people who first start climbing, thought that the most important attribute to climbing is strength. But in reality, climbing is a movement sport, where the ability to not only to move on the rock, but also imagine and visualize yourself as you move. In truth, men and women can both understand the movement part of the climbing, but men tend to revert to brute strength when they get in a jam on a climb. Women however will look for ways to move.
There is another reason why women tend to advance quicker as climbers. Women's center of gravity tends to be closer to their hips. One secret to climbing is to keep your weight distributed and your hips over your feet. Women, for some reason instinctively know this. Women will climb with their feet more than their arms and that makes them better climbers initially.
However, at the highest level of climbing, men tend to have a bit more of an advantage, whether it is height or strength, at the leading edge of climbing difficulty, men tend to excell a little more.