Note that you're responding to a different person. I didn't say the "not like conservatives are forced to get abortions" bit, and I recognize it as a fallacy. I fully understand why people who are against abortion see it as murder, and consider it as moral imperative to stop it wherever it happens. I was merely pointing out that this difference stems from the different views on what personhood is, not on whether a fetus is alive or not. No pro-choice person will deny that a fetus is alive, or that it's a human being. The sole question of interest is whether it is meaningfully a person, with the rights that entails.

If having brainwaves were sufficient to impart a natural right to life, we'd treat killing any animal with a brain as murder. We don't. So, no, that's not it.

And also, I don't know where the exact answer is. I do know for sure that anything without a brain is not a person. When it comes to brains, it actually intersects with the issue of personhood of animals, since at various stages of fetal development, the complexity and brainpower is analogous to that of animals. Now, I do consider it quite likely that some animal species have personhood. It is most likely the case at some stage of fetal development, as well. But we still lack the precise definition of what it is, to be able to draw a clear line. So for now it's "I know it when I see it".

With respect to your question on life support equipment - I do believe that there are valid cases involving brain activity where the human being in question is no longer a person, because the brain function has deteriorated (due to damage etc) too much for self-awareness. In which case, yes, I would consider pulling the plug to not be murder.