Who is responsible for the sex of the offspring male or female .why?

Only the male because when their 4 gametes are generated from meiosis, 2 will carry the Y chromosome and 2 will carry the X chromosome. 
The female's 4 gametes will all only carry the X chromosome. 
Males are only created when Y from the male gamete fuses with a X egg from the female. 
Females are only created when X froth male gamete fuses with a X egg from the female.

Male, because they select the gene because xx girl and xy is boy. so he chooses x or y.