If you change the correct portions of your genome, you would not be sterile, nor would you be dead. Your statements to the contrary are simply assertions without evidence. The evidence that I have that changing the correct portions of the DNA of a human results in a viable organism is chimpanzees. They have DNA that is ~99% identical to humans. Therefore, changing the proper 1% of the genome of a human results in a chimp, which is a fertile, viable organism. You may argue that it's unlikely that this particular 1% of the genome would be the portion that changes, and you would be right if random processes were all that were at work. However, natural selection ensures that of all the variations that occur, only those that are viable and fertile will survive to leave descendants. Mutations producing nonviable and nonfertile organisms indeed do occur, but we never see the products of such mutations. Please note that the particular mutation that produces a nonviable or nonfertile organism is just as unlikely as the mutation that produces a fertile, viable one.
As for your other objection that there would be no organism for a human that mutated to the point where interbreeding with humans was impossible goes, keep in mind that in reality, there are no large changes that occur in single organisms. Large changes occur over many generations in populations of organisms. Just to illustrate, suppose that there is some general trait that can be measured numerically and is characteristic of a species. Suppose that humans have a range of values between 40 and 60 for this trait. Now suppose a group of humans becomes genetically isolated from the rest of the population. The rest of the population can evolve in such a way that the value for this trait decreases to 35-55, while the splinter group evolves so that their range is now 45-65. Note that there is still some overlap between the two populations, so we don't characterize them as separate species. Further evolution in these directions though might result in a range of 25-45 for the main group and 50-70 for the splinter group. Now the two populations are separate species, without ever having a single organism that had no other organism with which to interbreed.