There are hundreds of logical fallacies, but these are the ones I most commonly see from TRP and TRP apologists. Feel free to add more if you have them. A similar list could be made for the far left end of the spectrum, but hopefully this helps illuminate distorted thinking patterns for all of us.

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Universalism.

Universalism is a concept that some ideas have universal application. In the context of TRP, this is mainly expressed as 'all women are like that', or AWALT. 'All women display this proclivity, or that trait, etc'. While there are gender proclivities and patterns in behavior, few are universal.

False Cause.

Presuming that a real or perceived relationship between things means that one is the cause of the other. This is another way of stating correlation does not equal causation. Sometimes correlation is coincidental, or it may be attributable to a common cause. Example: Girl dumped me right after I got emotional. Therefore she dumped me because I was emotional.

Cherry-picking.

Selectively choosing data points or clusters to support an argument, or finding a pattern to fit a presumption. Example: Women are hard-wired for hypergamy. Here is a small self-reported social study that proves it. (The result may be weak, there may be more robust data to the contrary, or no other studies replicating this result.)

Selection Bias

This is a bias that is introduced by a population sample that is effectively not random. Example: Guy dates only HB9 strippers and club girls, then concludes that all women posses their behavioral traits. Another example: "Guys who believe in TRP are all misogynists." TRP tends to attract a subset of men who may have had negative experiences with women, then reinforces their beliefs through distorted thinking.

Confirmation Bias

Perhaps one of the cardinal fallacies of TRP, confirmation bias is the tendency to interpret new evidence as confirmation of one's existing beliefs or theories. This is what keeps people in distorted thinking patterns. They develop a presumption or belief about women, then tend to see "evidence" of their belief everywhere, which only reinforces their position. In reality there may be much evidence to the contrary they are ignorant of, or they are viewing new evidence through a skewed lens because their mind is already made up.

Composition/Division

Assuming what's true about one part of something must be applied to all or other parts of it. Similar to Selection Bias and Universalism. Because we observe consistencies in things, our thinking can become biased so that we presume consistency to exist where it does not. You might see consistencies in the women you are dating and make the presumption that AWALT. Very easy to do, and easy to find reinforcement in TRP.

No True Scotsman

An appeal to purity as a way to dismiss relevant criticisms or flaws of your argument. Example: "No real Man would ______." "A quality woman wouldn't _______."

Poisoning the Well

Another pervasive TRP fallacy. Adverse information (be it true or false) is presented to the audience preemptively in order to discredit or invalidate any forthcoming argument. Example: 'X is the truth about women. Now, undoubtedly some bitter post-wall lurker is going to come out with a pathetic response to X, so pay her no mind.'

Genetic

Judging something as either good or bad on the basis of where it comes from, or from whom it came. Any argument from a woman can be easily shut down with the genetic fallacy. Even sound arguments can be made to appear fallacious. Another example: anything that comes out of RP Celebrity's mouth is gold.

Appeal to Nature:

Assuming that because something is 'natural' it is therefore valid, justified, inevitable, good or ideal. Many 'natural' things are also considered 'good', but naturalness itself doesn't make something good or bad. For instance there are many toxic or addictive substances found in nature. Example: 'Men are biologically programmed to spread their seed. Therefore this is a fundamentally natural and therefore good behavior.'

Appeal to Evolution

Very similar to Appeal to Nature, TRP loves this fallacy because it is so convenient and yet so difficult to refute in conversation. Much of evolution is extrapolated, and therefore easy to fabricate seemingly linear, logical claims that support your pre-formed conclusion. 'Women evolved to do this', 'men evolved to do that'.