"Strange though in the animal world it is not the female who goes out to attract the male, but the other way round."
That's only true in some species -- probably the majority, but not universally. A few bird species, eg the phalarope, have the roles of initial courtship and display reversed. Like many statements about the animal kingdom, we should be careful to avoid sweeping generalisations.
Also, men have nipples because, apparently, all fetuses initially develop as biologically female, until at about 5 weeks or so when the Y chromosome starts to impact development.