There's another subtle factor to all that, however, that changes it slightly.
Mark hates the clubs, and hates how they won't let him in. So he makes his own. That's pretty much the driving factor for a lot of his actions.
Then his best friend is going into one, which makes him bitter, jealous, envious, etc. Mark is a petty person.
However, Eduardo is still his friend. There's a key scene I missed until I listened extremely carefully--when Eduardo comes in from the rain and they are arguing, Eduardo is going on about how he's working hard in New York, and Mark goes, quietly and quickly:
"Facebook is here...You gotta move out here...I want, I-I need YOU here, Eduardo. Please don't tell him I said that."
(Him being Sean.)
Mark wants to look cool in front of Sean, with his new exclusive club. And he wants Eduardo to be a part of facebook--instead of those other clubs.
But...Mark, being so socially inept, didn't know how or when to tell him, and Eduardo doesn't even hear Mark's needy plea in the argument and it starts falling apart from there.
So yes, Mark WAS bitter about Eduardo getting into the clubs, but, in a way, Mark felt betrayed that Eduardo would consider those instead of his.