Do women approach men?In terms of relationships is everything up to the man?

It's hard for me to approach women and when I do it goes wrong I don't know why. I don't go to lugs and the women I know never call me it's always me calling them and they would call me on occasion. I dated a girl a couple times and made but I refused to call her I really don't care. I'm good-looking and I'm an enjoyable person for women not call me . The reason I'm single now is that I'm very introverted and I don't go out often . Now that I am it's seems hard for me to approach and when I do the women are nice but either have kids , been too promiscuous which turns me off or aren't my type and the one I really want. I met one chick who was very similar to me ,got her number(met her in a mall)text once she responded a week later I text twice no response I was too nervous to call earlier and thought to myself if she really liked me she would call why do I always have to call.Is this how it is the guy does everything?