By this, do you pretty much mean an Internet Tough guy? Like, "I'll hack you" and "Your a geek" insults?
No, although that may result in a ban as well.
"Too cool for the internet" is an advanced form of unaware hypocrisy.
The general procedure is as follows:
1: Get on the internet
2: Log in to the X Forum
3: Post that the internet is for nerds, X is for nerds, you don't care about X or X Forum because it is for nerds, everyone is a nerd except you, you are sick of being surrounded by nerds, everyone should go outside except you because you were just outside having tons of love.
Some examples from the ban list:
no one intelligent plays blockland i just use these forums to advertise the games i make
cuz its easy to get geeky kids with acne to play my games i rarely play blockland
Eh, I'd rather know the guy I'm blowing instead of some random 14 year old off the internet who makes stuffty add-ons and plays stuffty games in basically all of his day besides school.
I think someone's gunning for their next forum ban. 
Hahaha, do you think that actually bothers me? if it did bother me i'd suck your rooster like Daenth or whatever his name is.
The fact that in 2 out of 3 the poster is specifying what kind of rooster they'd like to suck appears to be a coincidence.
"Internet toughguy" and "Too cool for the internet" can also intersect, such as saying "I will beat the stuff out of all you scrawny nerds. All you do is play games all day I lift weights and stuff."
