Assumes women are "mentally weaker" which is not generally the experience most women have.
Certainly most women are aware that they are physically weaker than most men, but there are other things in life that make up for it (like living longer, having stronger bonds with your children, etc).
Nobody chooses how they are born. The more autonomous you are, the better choice you have on how you live. Most Western sociologists would tell you that women have far more practical choices about life style than men do - so, all in all, the answer is NO.