This question have been lingering inside my mind and I see some family blaming the woman for giving the husband a particular sex of children. And the woman will always be saying that it's what the husband gave her she is bringing out. Please between man and woman who determines the offspring.
Firstly, what's offspring, it's simply the young of a parent or progenitor. Your question is lt rightly put in place, you should have replaced offspring with sex judging from the context of your write up. The offspring is determined by both parents but the sex of a child is mostly determined by the father since his the only one that bears both the X and Y chromosome.
The female only has XX chromosome which fuses with that of the father to form the offspring. When the X chromosome of the father meets with the X chromosome of the mother, it's a baby girl and when the Y chromosome of the father meets with the X chromosome of the mother, it's a baby boy. Since it's only the man that has this Y chromosome, the sex of the child is determined by only the father. That's why you often hear, it's what you gave me that I gave back to you.