Your mother gave you 23 chromosomes but there was no Y in it. She has two XX. Only men have XY. If father gives X to new child then he creates female, if father gives Y he creates a son.
Only in sporadic situations, bad genes combination, one in 10,000 or so, a person can have too many chromosomes and instead of YX will have YXX. It is called chimera, and person can display both sexes characteristics. I'm not sure though if chimera can have children at all and pass Y to next generation. Anyway Chimera can be classified as both male and female, so this person is not your typical mother to transfer Y.