in what circumstances and in what kinds of society is being a mother
an asset for a womans status? and when is it a liability

being a mother can be an asset in terms of the transition to
adulthood.  in many societies the males have tests they must undergo
inorder to transform into men, women have childbearing to show that
transition.

Yes, Margaret Mead made a very strong case for this. Going by memory
she said both men and women to be happy need to be affirmed as members
of their gender. She said women were affirmed as women by bearing and
raising children, seems like she added this would be true unless women
were specifically taught differently.

However, men are not really affirmed by aiding in conception, (though
I know some men who think so...)

So she said every society must provide some means for men to affirm
their maleness. It is interesting that our society in the US has
pretty much made it illegal for men to have any unique role whatsoever
to affirm their masculinity.  Those who wonder what is wrong with men
today should try to understand this.

In years gone by, men were allowed to be primary breadwinners as a
masculine role. Gone.

In more primitive societies, men were allowed to be the warriors as a
masculine role. Gone.

Etc.