Would that advent of human cloning mean the end of "man"?

If human cloning succeeds (i.e. taking a skin cell from person A and cloning a new person, B), then it appears likely that the Y chromosome, with its measly 21 genes, might go the way of the dodo bird. Would there still be a need for men?

Edit: I’m not talking about the moral or ethical aspects of cloning, but rather, would the ability of women to clone themselves perpetuate the evolutionary loss of the Y chromosome?