First of all, it is not “considered impossible to extend human lifespans” by everyone. Nevertheless, in general, it is considered impossible to extend human lifespans because that is the way we are conditioned to think.
Science and engineering are the key to extending human lifespan, but they have only been around a couple of centuries or so and have not gained acceptance by the general public. The masses turn to religion and superstition to assuage their fear of the horror known as death. They send their money to TV evangelists who promise them salvation via an unproven package of lies that appeals to their fear of death and desire for meaning in life.