You are misrepresenting feminism if you say that it generally pushes the "woman weak man strong" symbolism forward, major feminist thinkers (that I know of) are precisely arguing that this symbolism pervading society must be overturned and is in large part the basis of female subordination.
And yet feminists constantly propose legislation that amounts to special pleading, because "woman weak, man strong". Again, this isn't all feminists, but it's certainly a fair amount. This isn't a new split in feminism either, it's been going on for quite a while now.
So many insults that mean feminine mean weak, this is a proof amongst others that this dichotomy exists. Actually that's another phenomenon that points to a patriarchy although probably still not proof in your eyes, I don't have statistics, but I bet you know what I'm talking about. If the symbolism attached to female means weak and the symbolism attached to male means strong in a majority of people's minds, then there is a patriarchy. An intelligent feminist insists on the point that the patriarchy, whilst it means that power is inherently associated with having a penis, actually hurts men also, because as victims in a classically "feminine" situation, they will not be taken seriously.
I wouldn't argue against the idea that the dichotomy exists and that insults can be used to reinforce gender roles, but I don't think there's anything patriarchal about that. General trends in behavior
do exist and are observed and commonly known. It's unusual for men to exhibit traits typically associated with femininity and vice versa. Similar how heterosexuality is the normal (i.e., usual/common) sexuality calling someone a "fag" or "dyke" is also used as an insult.
These types of insults are typically hyperbolic and used against people for whom they don't typically apply, otherwise they're not really effective as insults. It's not really insulting to call an openly gay man a "fag" or "pretty boy". In the case of insults that, while are gendered, are not
entirely gendered, they can be used against mostly anyone and have different meanings depending on who they're used against. Examples of this would be words like "bitch" and "dick". Calling a man a "bitch" is really two insults in one, as it's an attack on his gender identity as well as his character. Calling a woman the same is just a character insult.
I don't subscribe to the idea that we're blank slates, nor do I subscribe to the idea that they're anything
wrong with people who don't fit the typical roles. I do, however, subscribe to the idea that these roles
are typical. I don't think we should be trying to encourage more people to become gay, more women to become muscle-y, or men to become emotional simply to make it more common. Even worse is enacting legislation that treats people differently based on what's typical, specifically because there's nothing wrong with not conforming to the typical. Differences are fine, though they will be observed and often mocked.