He has paid his taxes already. By renouncing his citizenship, he had to pay an exit tax on his entire estate at time of renunciation as if it were cash. That is what it takes to renounce.
He will have already paid capital gains on unrealised gains. Even if he never sells his shares in Facebook, he has already paid capital gains on it. If, by the end of this year, Facebook shares tank to half their current value, he would have already paid almost twice as much as he would have had to had he remained a US citizen.
(By the way, the USSR, Nazi Germany, and Cuba impose(d) exit taxes on people seeking to leave, so the USA is in good company.)
The only tax advantage he gets from renouncing US citizenship is a future advantage on future income. As an American person living abroad, he cannot legally make any tax efficient investments (even in something as simple as an IRA or pension – without a US address, he can’t have a US account), any money he would put in a foreign IRA-equivalent is taxable by the IRS as income. Or take advantage of tax breaks for investing where he lives, as the money he saves would be taxed as income by the IRS. The only thing he could legally do living abroad is buy stuff and open a checking account (and even that is about to be limited thanks to FATCA*.)
Imagine it this way: What would you think if a rich person from France decides that they are never going to live in France again, and he decides to become an American and wants to invest in US businesses when he gets there. But once he is living in America and paying American taxes and investing and creating new jobs through various tax efficient incentives, the French government presents him with a yearly tax bill for all the money he saved by taking advantage of the US incentive schemes – and it will be that way for the rest of his life. He is less likely to want to invest where he lives. The most he will do is spend money living it up. He will not be creating businesses and jobs.
The US system of taxing people on all their worldwide income is shared only with Eritrea, and even Eritrea only charges 1% on worldwide income…The US charges 35% after the first $95k on all worldwide income and investments after they have paid local income tax (thanks to US tax law, I, for instance, would effectively pay 75% income tax on any income I have here in the UK above $95k.) And because Americans abroad cannot invest in the US without US addresses, and they cannot make tax free investments where they live, and their absentee ballots never get counted unless the race is close in their state, Americans abroad effectively suffer taxation without representation.
I own a small business, I never earn more than the threshold of the $95k foreign earned income exclusion, so I never owe tax. But I have to pay a tax attorney (not an accountant as it is too complex to comply,) about $1000 a year in order to make sure all my US paperwork is filled out correctly. (If it isn’t, I am subject to fines equivalent of up to 300% of my entire estate.) What kind of free country does that to people?
*FATCA is the equivalent to a financial Berlin Wall around the US. Anyone who ever paid tax in the USA, no matter where they live, may find it difficult to get a checking account outside of the US after 2013, because in order to comply with FATCA many banks are deciding not to take on American customers as it is cheaper than to implement the complex systems it would take to track the financial transactions of their American customers.