It hails from when family lines were important, and you can practically only have one line reflected in a name. Unsurprisingly, most societies considered the male's name to be the dominate lineage of interest, although that doesn't hold true 100% of the time.
> you can practically only have one line reflected in a name
Not true at all. You can trivially have two family names in a full legal name. In fact many cultures do exactly that to this day.
Also worth noting that the male's name being preferentially propagated makes a lot of sense in a society where the best off frequently inherited their vocation from their fathers.