A Mitzvah does not necessarily indicate a Chiyuv. There is such a thing as a Mitzvah Sheaino metzuva v’oseh (A Mitzvah which you are not commanded to do but you do anyhow). This means that you are doing something praiseworthy and you receive a reward for it, but you are not OBLIGATED to do it.
Most of the Mitzvos that are incumbent on men but not women fall in the category of Mitzvah sheaino metzuveh v’oseh for women. I am not obligated to shake the Lulav & Esrog or sit in the Sukkah on Sukkos but if I do so, I am fulfilling a Mitzvah and do receive a reward. And if I’m Ashkenazi, I even make a bracha saying the words “And He commanded us” even though I personally was not commanded and have no obligation to do it.
There is also something called a “Mitzvah kiyumis” which refers to something that is not obligatory on anyone but if someone does it, they are doing a Mitzvah and receive a reward. For example, Rav Moshe Feinstein holds that the Mitzvah of living in Eretz Yisrael falls in this category, and while it is not obligatory, one is fulfilling a Mitzvah if he does so.
Of course, one can argue that if something is a Mitzvah even if it’s not obligatory, why would someone choose not to do it? And I think that the answer would be that their priorities and “cheshbonos” would be different. For example, if there is a particular Mitzvah that I am not obligated in as a girl, and there may be hashkafa problems (i.e. feminism) with my doing it, then it would be a bigger Mitzvah not to do it.
In the case of marriage, according to halacha, a girl can decide that while it is a Mitzvah to get married and have children, it would not make sense for her to marry someone whom she does not want to marry (for whatever reason) in order to fulfill this particular Mitzvah. While a boy should also not marry someone whom he really does not want to marry,it seems to me that his reasons would have to be more substantial than a girl’s would since he does have an obligation to get married.