I climb over 600' in a mile with some sections close to 15% on my way home from work every day on bikes that weigh over 40 lbs, not counting what I'm carrying besides that.
Honestly, my athletic ability is probably below average for a cycling enthusiast as I don't train and prefer to ride at a relaxed pace yet I can do it, and don't feel the need to take the longer, easier route. Like they say, "just do it".