The penis controls men (males), but not in the way women expect.
.. and probably not in the way men understand.
All men have penises and testicles. This is obvious, but particularly important here. This is also to say that males without these are not men. For this post, this is particularly true. Notice how I said "men" and not "male". A man with two missing toes is still a man. A man with two missing testicles is not a man, only a male. With hormone therapy he remains a man. It's the hormones, the very biology of being a man (as opposed to a not-man), which is being discussed.
Testosterone, produced in the Testicles, significantly increases through male puberty. One of the other side-effects is a sort of semi-permanent erection for boys going through puberty. All "real men" come from this background.
Boys learn to control their puberty-erections; walking around with a hardon isn't socially acceptable in the least. Again, boys learn self-control.
This self-control is a thread tying all men together. It is not some cabal of elders deciding it. It is the social pressure and self-esteem to resist biology. Men do not pressure one another. Men don't walk around with hardons. They don't, because as boys they learned self-control. This is a part of what it is to be a societally-integrated man. Men don't even "learn" this, they "develop" this each on their own with zero interaction with others. Men develop this self-control so well that it's completely past awareness. Because of having developed this, some things remain.
The remnant is noticed in men's "lack of emotions". However, men aren't passionless like women think. Men are reigned-in. The same control of emotions necessarily developed through puberty is continually developed as a man ages. Men build on the things they're used to and are good at. The side-effects include logic and reason. These seem to come standard in many men, evidenced by the concept of things like "the male handbook", e.g. the standard male rules of escalation. If women have similar things it's ineffable by men. (Females don't have rules of escalation, Horrible homilies)
The difference between men and women ∞
Again I say that biology forces men to have developed a psychological and mental self-control that women are never forced to develop. In comparison, women are emotionally "out of control". There is no equivalent in girls to the erection-mechanism in boys, and therefore women don't have the same remnant self-control that men have.
It could be argued that pubescent hard nipples for a girl are an equivalent to pubescent erections for a boy. I don't think these are nearly as obvious as an erection, and women at least have the option to wear a bra which will help. Furthermore, women get "hornier" as they approach menopause rather than as they enter puberty, so I don't think there is a commonness equivalent.
I would agree that there are separate opportunities/requirements for self-control outside of biology, and I can predict several arguments there. Things like ogling, flirting, cat-calling, approaching and the like. Think about that though, it's okay for women to do all of these things and not always okay for men to. Like with the biology mechanism, there is nothing reining women in. Hell, women sit back and insist that men do these things so they don't have to.
Could this change over time? ∞
Perhaps, one day in the future, men won't get puberty-erections because they will have biologically changed. Evolution of one kind of another might make this possible. I seriously doubt it though, as there is no selection pressure and absolutely zero biological history for this possibility. Examining primates might help, but I seriously doubt it.