In ancient times, but why was male dominance an across cultural phenomenon between most different civilizations?

It wasn't' the same everywhere, and it varied in intensity. Women had equal rights in Egypt, or at least it looks that way, and judging from the frescoes in Crete, women were quite free. Male dominance in Athens was extreme, but in Sparta women were scandalously free.
Among primates (and we are primates), male dominance is very typical, and it certainly is in the closest primate species to us, namely chimps. With chimps it seems to be might makes right, and as male chimps are bigger and stronger and more ferocious than the females, they dominate. Probably in human societies too males dominate because they are more willing to use violence.

Could you possibly word your question better? Most of the above answers will suffice.

Males are, on average, bigger, stronger and are capable of violence and aggression at levels most females are not. It's a biological thing, not a cultural one.

All those men had mothers.

The average basal metabolic rate is about 6 percent higher in adolescent males than females and increases to about 10 percent higher after puberty. Females tend to convert more food into fat, while males convert more into muscle and expendable circulating energy reserves. Aggregated data of absolute strength indicates that females have, on average, 40–60% the upper body strength of males, and 70–75% the lower body strength. Females are taller, on average, than males in early adolescence, but males, on average, surpass them in height in later adolescence and adulthood. In the United States, adult males are, on average, 9% taller and 16.5% heavier than adult females.

Men can not breast feed a baby and being pregnant kind of makes fighting a war or chasing down dinner a bit difficult.
Just for the record Matriarchy is not a new thing. Several societies in history have had the woman in the dominant role/s. Then there are also societies through which the linage, property rights and several other things determined by who the mother is (not the father).
For your consideration:
https://en.wikipedia.org/wiki/Matriarchy#History_and_distribution
https://en.wikipedia.org/wiki/List_of_matrilineal_or_matrilocal_societies

Dominance is a result of nature. Plants, animals, humans. It's not a social ideaology. Dominance has exsisted long before humans ever came to being. It exsisted when the first life forms appeared.

Men are physically stronger than women so they could dominate. Plus women were busy being pregnant, doing the cooking, cleaning, laundry, child-rearing, sewing, gardening, caring for the sick, etc.

because they weren't soy boys back then

Not necessarily so. Early Japan was a matriarchal society.