Why do they call marriage matrimony instead of patrimony?

From what I understand, matrimony comes from the latin word for ‘motherhood’ and this word defines marriage, a ‘correct’ union between a man and a woman (in the Christian god’s eyes) because it will lead to children, through motherhood.

The Online Etymology Dictionary says,
“c.1300, from O.Fr. matremoine, from L. matrimonium “wedlock, marriage,” from matrem (nom. mater) “mother” + -monium, suffix signifying “action, state, condition.” Related: Matrimonial.”
Patrimony, on the other hand, relates to inheritance. Isn’t it awesome how history and culture bleed through language?

That’s funny because if the union leads to children, then fatherhood is also a given… hopefully for the guy who is actually involved in the matrimony.