Why do arrogant people hate arrogance?

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I've had many friends come and go over the years and encountered many arrogant people, they won't hesitate to try and impress their world view on you, and tell you how people should and shouldn't be.

One thing I've noticed during their monologues and rants they all seem to have this common ironic trait, a hatred of arrogance and conceit, the very behaviors they show themselves, some aware of it, others unaware, some just flat out refuse to believe they are arrogant, I was friends with one guy quite a few years ago who would broadcast himself as humble and down to earth, and constantly points out and rants about traits of conceit he hates in other people.

One of my other friends says he can not stand arrogance, yet won't hesitate to tell me how many women he has slept with, and how sexually experienced he is and losing his virginity at a young age and how much he can drink. He sees himself as more enlightened and tries to educate me in his way of thinking, and has even gone as far as to say even tho I'm a few month older than him he sees me as a younger brother.

Another thing, they all seem to have that one person they can't stand, they will rant about them, usually another arrogant person, they will psycho analyze them, talk of their despise for them, but at the same time try to brush of their significance.

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I'm sure I heard a quote once that remained with me, but I'm not sure how true.

"People see in others what they are themselves" ... or may be I made it up.

I have noticed this, someone recently said "He drives me mad, he's always after the latest thing, bike, jacket etc that comes on the market" This was someone I'd known for a long time talking about her 14 year old son. I didn't bother to remind her that she too always has to have the latest thing, designer handbag, latest music etc..
I thought it was funny that she didn't know she was just like that but someone else she'd noticed like that got on her nerves because of it. So maybe people see things in others that they are themselves but fail to see it in themselves. I wish I'd said "Well you're like that too" to make her think. I think they don't realise, until someone brings their attention to it. Someone said it to me once and I didn't take offence it just made me take a look at myself.