Your woman just described Athol Kay married man sex life approach to red pill. It's pretty much the only method to red pill relationships. I'm finding it interesting finding the balance of alpha and beta.

They can be both. TheRedPillRoom's "Wolf Alpha" archetype for example.

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Start acting "alpha" to your boss or professor, then come ask again.

So that was tongue-in-cheek, because the two are not mutually exclusive. But they often are. As /u/redpillschool is fond of saying, this is a stochastic (probability-driven) rather than deterministic (hard-rule) process.

• One great way to be a good provider is to study something in STEM. This requires a lot of time investment, and gains you basically nothing but money in terms of attractiveness to women. Worse, preselection means that the rich get richer and the poor get poorer, so an early disadvantage can stay with a guy and multiply on itself for years.
• Another problem with STEM is that the field rewards you (at least more than others) for being right. If you know how to build rockets, and Joe next door builds crappy ones but has game---it doesn't matter. Joe will get fired. So you get rewarded for getting the right answer. When it comes to attraction, however, you can be totally full of shit and still get laid. Obeying the rules of one environment while in the other is going to lead to problems.
• Schools and the corporate world both reward compliance. Women do not.

why can't a guy be both Alpha and good provider?

Because an alpha has options, which means he:
1) has no need to commit to anyone to have regular sex
2) can have sex with a lot of women, but can only really commit to one
That's why it's easy for a decent looking woman to have sex with an alpha, but much harder to tie one down, only the top of the SMV ladder will manage to do that, but all wish they could. Scarcity is responsible for the alpha/provider dichotomy, not the fact that one can't be both.

Would you build the best castle in the world and let a trojan horse in?

I keep the keep the gates closed and occasionally, with my full knowledge, allow a limited number of enemy scouts in to scope around and confirm how impenetrable the rest of my defenses are, they don't know that I planned their entry, and I allow them to leave unscathed to report back that all defenses are operational and for the queen of the sister city to maintain the current diplomatic climate of submissive allegiance.