Some stereotypes are based on ignorance or malice. Other stereotypes are based on Statistical Reality. But even the latter stereotypes are deeply flawed in many individual cases.
In my opinion, women are generally more sensitive then men. I am not sure if there have been any studies on the subject, but it seems to be the case. Nevertheless, it does not mean that there are no men who are more sensitive then most women. One picture is worth a thousand words:
This 155 kg Autistic male is more emotional and sensitive then 90% of women and 99.5% of men. Thus, he will never fit into society which expects him to follow male gender roles.