Wrong. Halacha explicitly tells us the reason and it isn’t what you said.
See the Rambam on the Mishna Horayos 3:7.
“You already know that men are obligated to keep all of the commandments while the women are obligated to keep only part of them, as is explained in Kiddushin (Mishna 1:7) and he is [thus] [a man and a woman] are going to drown in a river, one should save the man first”