In this immortality speech, Richard Dawkins disputes the idea of living forever through medical advancements. While Dawkins acknowledges that this is not currently an issue, he predicts that as time goes on people will look for ways to prolong life by hundreds of years.
Dawkins knocks the idea of living forever because he claims that it's irresponsible. It calls for a cease in birth rates, which have showed no signs of slowing. The more living people there are on Earth, the more resources will be needed, so over-population would quickly become an issue. Dawkins also points out that it would be rather selfish to tell people to stop having children so that others could live forever.
This topic may seem a little bit like science fiction, but Dawkins believes that this is something that many people are intrigued by. Perhaps that's because people have an inherent fear their own mortality.