Using the word "tyrannical" is hyperbolic, but yes, the patriarchy exists. I don't really have the energy to engage in this topic hardcore right now, but I'm sure coreander is.
The best argument I can put up right now is that men are undoubtedly pushed into certain social positions and roles, while women are as well. I know I have also read studies about women in politics, for instance, and how they are held to a different standard than men are. This can also be empirically demonstrated.
I do think that even in a patriarchy-less world, women and men would occupy different jobs overall. On the other end, I don't think women are making decisions today in terms of their career free from societal norms. The answer probably lies somewhere in the middle.
My point from earlier was that if you buy into the redpill stuff, you also believe in the core ideas of the patriarchy. I will defend that statement.