> Currently there is a gender asymmetry in that maternity leave is normal (and required by law), but paternity leave is frequently non-existent, or discouraged.

In the US, at the federal level, maternity and paternity leave (both unpaid) are covered by the same mandate (FMLA).

In California, paid maternity and paternity leave are covered by the same mandate.

That doesn't negate the social asymmetry, of course.