What are cases for and against euthanasia?

Of people with serious disabilities. Not just like mild downs syndrome or being in a wheelchair, I mean like blind, deaf, mutes. Some kids are deaf, and they don't have the brain capacity to learn sign language and therefore can't learn much. If a baby is born and can't breath on it's own or hear, why do people keep it alive or name it? I don't really have a side on this issue, but i'd like to hear SERIOUS reasons why people take their side (saying "everybody has the right to live" or that "mentally challenged people are smarter than geniuses" is BS) Thanks for the answers! NO TROLLS PLEASE.