THERE IS NO PERSON ALIVE. Your statement applies both to unborn humans and to brain-dead adults on life-support, entirely because persons are minds, not bodies. However....
INACCURATE.
A fetus is generally very much alive, exactly as the human body of a brain-dead adult can be very much alive. In the future that adult human body could be a good candidate for a brain transplant --if it receives a living brain that replaces the dead brain, then the whole body could get up and do things again. Such a result would obviously be impossible if the body was dead, instead of alive! A fetus is generally a living human body, very much like that brain-dead adult body. The fact that no person exists, associated with that body, does not mean the fetal body is not alive.
INACCURATE AGAIN. Brain activity does not equate with personhood --see any of a great many ordinary animals, from rats to cats and dogs to hogs, that have significant brain activity yet don't qualify as persons.
The type of brain activity matters a great deal! --and no human acquires person-class brain activity until quite a few months after birth --
often 18 months just for this one aspect of personhood.
WITH RESPECT TO UNBORN HUMAN BRAIN ACTIVITY, ITS EXISTENCE IS IRRELEVANT TO THE LIFE-STATE OF THE UNBORN HUMAN. The body is alive from the moment of conception, period, and can die at any time afterward (
actually Naturally does die about 2/3 of the time, before birth). And as indicated above, unborn human brain activity is also irrelevant to its personhood-status, too, simply because no unborn human can ever have the type of brain activity associated with personhood --their brains just don't have the brainpower for it, and must grow for a long time, to acquire the necessary minimum brainpower (again see above regarding 18 months after birth, and just one type of personhood-associated brain activity).
IT IS ALWAYS POSSIBLE TO KILL A BIOLOGICAL LIFE-FORM. Your body does it routinely, killing invading bacteria by the thousands every day. "Life of a body" and "life of a person" are two totally different things! A True Artificial Intelligence, for example, will not have a biological body, but it will still be a person that is as
**mentally** alive as you or I.
THAT SAID, IT IS NOT POSSIBLE TO KILL SOMETHING THAT DOESN'T EXIST, like the personhood of any unborn human. As mentioned above, humans only acquire personhood after birth, and therefore it is impossible for the unborn to have personhood, and therefore it is impossible to kill that personhood. But don't confuse "personhood" and "biological life", because they are two very different things!
IT IS DEFINITELY KILLING A LIVING BIOLOGICAL ENTITY. But it in no sense is killing a person, as just explained immediately above, because it is impossible for an unborn human at 30 weeks to have personhood.