Well, men and women both have testosterone and estrogen in varying degrees. Were you talking about mannerisms, or genetic traits, or what? Crying at a movie, or a penchant for quiche?
I think that despite some peoples dislike for the gender division of qualities, they exist and no amount of denial is going to change that. So there are some women who exhibit “masculine” qualities, ie; they wear their hair extremely short, work in traditionally male jobs, wear masculine clothing, etc. One can say the same for men. Some guys are more comfortable stepping out of the traditional “male” roles that society has laid down. They can wear a pink shirt, spend time in a book store or flower shop, all sorts of things that are/were traditionally considered “feminine”.
Our society discourages men from the beginning of their educations from showing emotions and expects them to “be strong, take it on the chin.” It’s part of the very fabric of our culture. but for many years now, we have been trying to counteract that on an individual basis and the numbers are adding up to more and more men secure enough in their masculinity to step out of the traditional expectations and be more in touch with the part of them that society dictates that they repress.
Short answer: Yes, men have a feminine side.