Namely, the relationship importantly (to the story) does not go well, and Zuck's redemption is being able to overcome the fraught relationship with his old-money investors.
In the world of the movie (which again, is not real life), the cost is that Mark Zuckerberg will never be happy. I'll admit, it's convenient to believe that the billionaire seems to have achieved what he wanted but at the cost of everything that actually matters to living a meaningful human life. And yet it may have a grain of truth.
To many others, that social status is achievable in different ways -- athletics, personality, appearance, or is even inherited (name, money, etc.). So many, dare I say most, people joining the Finals Clubs don't have to make the kind of sacrifices Mark did because they just naturally fit in. And as a result, membership of those clubs is less of a "big deal" because they didn't have the mountain to climb to get in it.
In Mark's case, he didn't have any of the above to achieve that. But he found out he did have a really unique and "cool" way to socialize -- the social network. The popularity and notoriety from the things he did contributed to his "cool" status on campus. And as we all know, the money and power he got from it cemented his status as a "cool" kid with status.
What's wrong with Mark Zuckerberg (the character) is that he doesn't want to be cool, he wants to win. He resents Eduardo for "beating" him by getting into the Phoenix. What matters is winning, and to be fair to him, that's what Harvard is all about. It's about having things that other people don't. And while most Harvard students who I know, once they got there, accepted that they were going to be the middle of the class within the top of the class, some people have something wrong with them and they can't stop.