“Hashem gave specific and different characteristics for each gender for them to fulfill their respective roles.”
This is true. There are about a dozen mitzvot that HaShem gave to male Yisraelim that he did not give to female Yisraelot. But for most of them, female Yisraelot are encouraged to do them (such as hearing the shofar) and the normative practice is that a female Yisrael will even say the blessing beforehand if she is Ashkenazic!