living forever would lead to our extinction ... in along run our genome would adapt and we would become sterile
Evolution does not work that way. Evolution does not refine beyond what is good enough, it does not refactor. Genomes do not adapt, genes which encode phenotypes that are best at getting its owners to maximize reproduction with respect to an environment are selected for.
Most importantly, if we could cure aging and necessarily cancer, then you can bet we would have the sophisticated understanding of genes, proteins and cells required to fully control our genome.
I tire of statements like this. Either you have no capacity for exaggeration, or I have grossly misunderstood and the docking is actually more momentous than the discoveries of fire, DNA, germ theory, cell theory, flight, and nuclear physics combined.
Now, if we figure out how to beat aging and live forever, that is something whose impact might be difficult to overstate.