Don't you think the stigma that a man has to pursue a woman is unnatural?

No, I think it's perfectly natural. If a woman is not interested in a man, it's up to her to have a backbone and make that plain, and not give in to unwanted advances. A guy should be able to tell when a woman is interested and playing coy, and when she's really not interested at all. Males are meant to pursue females, not just in humans but just about every species on Earth. So yes, it's very natural.