I see it as a conversation happening both ways. It just depends on who is the initiator of the conversation.
Consider for example the following two imagined scenarios:
In order to send a new tweet:
1) You click a button that says "Send My Tweet".
2) You click a button that says "Send Your Tweet".
In the first case, you are telling Twitter to send the tweet you just wrote. The power lies with Twitter to send it.
In the second case, Twitter is telling you to send the tweet. In this case, the user has all the power.
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It's interesting to compare Facebook's approach with Twitter's:
Facebook is a bit of an oddball in addressing the user. Facebook usually addresses the user as "you", but it sometimes refers to the user in the third person. On the home screen, it asks "How's are you doing, Sean?" and displays the link to your profile as just your name. On your actual profile page, if you hover over the Activity Log button, it will say "See your activity on Facebook". But then when you go to privacy settings, it says "Who can see my stuff?". This makes a ton of sense. By using "my" instead of "your", Facebook is making the user feel like they have control of their stuff.
Twitter is pretty squarely in the "Me" camp, as evidenced by the link to your profile on the top of the page.
If the website has something informational to tell the user, like a notification, they will always refer to the user as "you".
For example:
"Bill just retweeted you", "Bill just liked your status", "Your page is undergoing maintenance".
When you're changing account settings, the website will invariably refer to the user as "you". You are the one who actually needs to perform an action.
For example:
"Change your password", "Update your email".
The vast majority of people (at this moment in time right now) would never, ever think of paying for a social network. That would be akin to asking them to pay for their Gmail account. It's just not going to happen.