(Comic via SMBC.)
At some point in the future mankind will figure out how to live forever and I am convinced that that is what will cause the final destruction of our species. I know that sounds contradictory, but just hear me out.
Society currently has a way of refreshing itself every 20 years or so and that it called "Kill off the old fuckers and make some new babies." It's not the most efficient method in the world but it has served us well for the last several millennia. This is caused by strange bit of brain chemistry. Almost all of your beliefs about the world are set by your mid 20s. Not set like concrete but set more like a tasty jello mold. Your brain is done being bombarded with hormones from puberty, your pineal gland calcifies around the age of 23 (fnord!), and after that it is almost impossible to change someone's view of the world. Once you hit your 30s you are set in your ways and your personal narrative is a third of the way down its path.
What's good about this though is that during their teens and twenties most people are open-minded, liberal, tolerant, and willing to consider new ideas and try new experiences. Every generation says, "Let us strive to be better than our parents!" But also says, "Hey, let's not take this too far." And so, society changes by generational quanta. Things never progress steadily but in small leaps. And not always for the best but always in a new direction. Each generation has their own memes, causes, art, and beliefs that makes the culture has a whole just slightly different.
Immortality would mess this up is that we would miss out on the "Kill off the old fuckers" part. People with antiquated ideas would linger on for eternity. Just imagine your grandparents not only alive but healthy, active, of sound mind, and eager to vote. Ok, now imagine your great-grandparents alive, healthy active, of sound mind and eager to vote. And now your great-great-grandparent. And so on. Immortality would change the average age of humanity, if not the mean age. Over time young people would be forced out of the marketplace of ideas. We would have the equivalent of not only geocentricists, as in the comic at the top of the screen, but also people who still think slavery is a great idea, that women should never leave the home, and think that germs are "just a theory". (Wait, we still have the last two.)
At any rate, society would quickly stagnate. New ideas would never stand a chance. We would repeat the same memes for eternity. Nothing of interest would be produced without everyone complaining about how derivative it is. Hopefully people would refuse the immortality treatment or start to kill themselves out of sheer boredom.