You could not possibly be more wrong if you were actually trying to be wrong. And you are completely and utterly wrong.
A man is a man. A woman is a woman.
A man or woman who by injury, illness, age, or defect is sterile is still a man or a woman.
The sexual union of a man and a woman, considered in the abstract, is capable of producing children. It is therefore, in the abstract, the substance of which marriage is made.
Physical gratification conducted between two men, or between two women, or between a human and an animal, cannot EVER by its very nature produce children. Relationships based on such actions, therefore, are not the substance of which marriage is made.
Your argument confuses substance (man, woman) and accident (sterility due to age, injury, illness, or defect). Such confusion is quite common in this miseducated age.
Hmmmm, maybe you should learn how to communicate more clearly since you said the only valid reason for marriage was to have children.