> > Essentially "I am rational therefore I am right".

> Sounds like basically the entirety of philosophy

That's the opposite of the experience I've observed.

The starting point for a lot of philosophy students is learning the teachings of Plato and Socrates, among which the most famous is likely "I know that I know nothing"

The spirit of searching interrogation is there, along with Socrates' daemon who, Socrates said, prevented him from saying anything untrue (I'm hamming it up here).

The philosophical prototype of Socrates also gives license to be a gad-fly, piss people off for a good cause, etc. Instead of offering to pay a modest fine when he was found guilty of corrupting the youth, Socrates was so certain of his rectitude he told the court he should instead be awarded free meals for life like the Olympic champions. Now there's someone with chutzpah.

There are plenty of schools of thought that start with "I am not likely rational" or "I can't know if I'm rational".

not really. It is a specific school of philosophical thought - and the basis of a lot of the critiques of science, positivism.