The comparison is not of the same type. The fetus needs the mother to develop. In fact, if you kill the mother, the fetus will indeed continue, just not for very long. As for tumors, human life requires a degree of cell differentiation that the fetus has but the tumor doesn’t. Since a tumor is identifiably different than a human fetus, and will never become a human person, it isn't relevant to the discussion.

As for the conclusions driving the argument, that's just a natural hazard of any debate. A big issue like abortion is like a labyrinth, or a maze, with dozens of turning points and forks in the road. Each debater has (we hope) already gone through the threads and tunnels of the labyrinth themselves, and reached their own conclusions. But in debate, you meet opponents back at various forks in the road. That's where you haggle to go right or left on each sub-issue. It makes it seem like you all just got there together, and all for the first time, but that's just an illusion. Instead, you wind up urging your opponent to head toward your conclusion.