Alternatively, realize that repressing that urge to be an alpha male because that's the current high-brow societal pressure is isomorphic to being a gay guy in the closet ;)
You clearly have zero idea what it is to be a true "alpha" male. The societal stigma you alluded to is levied on toxic assholes.
I would contend that there's a great amount of collateral damage, and that 'toxic assholes' are those least (genuinely) susceptible to social pressure.