When you find yourself reluctant to sit on a chair because it had unexpectedly collapsed in the past you might shake your head and think "there, I'm so irrational!". But your reluctance to sit on a probably rickety chair is not irrational - you think it's irrational because you have a false view of what irrationality is.

I don't think we are all irrational every time we fail to see through an argument in a book, but suppose it's true about you. You are still more rational than you think you are. You are irrational in a minor way - believing a misguided theory of the nature of rationality - but rational in a major way - you respond well to probabilistic evidence as you go through the day.

If I make a stupid decision but don't execute it because I'm, say, lazy, then I'm lucky, not rational. However, at other times a person acts for good reasons just as she does what she thinks she shouldn't do, not knowing that they are good reasons. Just like sometimes we are a lot less rational than we think we are, it is also true that sometimes we are a lot more rational than we think we are.

I don't think any of my desires or beliefs or other mental states are external to me. Many people will occasionally feel alienated from the motives for an action - "whatever possessed me to do that?". Note, however, that some people feel alienated from the white hairs that recently appeared on their heads - "who put them there?", they might ask the mirror - but the white hairs are still theirs. Similarly, I might feel alienated from an action or a mental state because it does not fit with my visceral self - image.

Suppose a student of mine writes in her exam that "morality is completely relative to culture, so nothing is absolutely right or wrong. Because of that, it is absolutely wrong to be culturally intolerant". This student, if she believes what she writes, believes a contradiction. She ought not to believe the contradiction - it's a basic epistemic norm. This is true even if she can't avoid believing it - no amount of studying will show her the light.

Incompatibilists will tell you that a work of art has no meaning unless the artists could have chosen to create a different one, but actual artists often say things like "the book chose me" - that is, the work had to be. Some philosophers would call it "volitional necessity", and a similar case that's discussed is the case of Luther saying "here I stand, I can do no other".

The fact that only humans above a certain age can be morally virtuous, rather than babies or cats, means that that being moral requires some cognitive ability. If virtue is about desires, it is worth remembering that you can't desire some things without being able to conceive of them. Suppose a virtuous person will desire to make people happy and desire to tell the truth. You can't desire to make people happy without having the concept "happy" and you can't desire to be truthful if you don't have have the concept "lie", so a cat or a baby cannot desire these things.