Everybody has their own personal reasons for expatriating, but here are some of the benefits:

1) Freedom from the global US tax net. Taxing you no matter where you breathe on this earth is wanton American exceptionalism. What other nations don't dare do to their citizens, the US government doesn't think twice about. Once you renounce, it's your choice either to live the rest of your life free of any tax net, or to pick a place you want to be year-round and opt into the tax system (assuming it's not a tax-free jurisdiction). If you do, you'll at least know you have the freedom to walk away from it by simply moving elsewhere.