You are thinking about individuals. But you ought to think about nations. Imagine that the discovery for life everlasting was made in the United States.
What do you think the first reaction would be of Vladimir Putin? And of North Korea? Furthermore, how do you think the Middle East will react, if they learn that their collective enemy number one and its perceived lapdog(read: USA and Israel, and yes, I am polarizing it a bit) have access to a way to live forever?
And how do you think religious leaders would react? Because life everlasting will pretty much mean that the core concepts of every religion will have to be reconsidered, since they are null and void. Take the concept of Samsara from Buddhism. Or the idea that every man or woman will be judged upon their death that is pretty much the core of every other major religion.
But even if THAT wouldn't cause upheaval, how do you think that, say, the Catholics would respond if the Protestants had the means to life everlasting? Or the shi'ites, if the sunnites would have it? Or the christians, if the muslim would have it?
But even if you stick to your own scenario, how do you think the poor would react if they learn the rich and powerful will have an unlimited lifespan?