You see the situation backwards. The idea that a person doesn't exist until later through pregnancy or after birth is the easily critiqued millennia old dogma. The last century and a half of medical technological advancements have given us clear ways to distinguish a fetus as distinct from the mother and show the continuity of existence back to conception.
What's this? More vague, vacuous recieved wisdom devoid of actual substance or specificity. Imagine my shock..
There is an incredible irony in the fact that you are arguing for a clear separation between a fetus and its mother while also believing that actually creating that separation should be illegal..
In reality, the status of a fetus is, again, very obviously liminal. It is not a distinct organism and not an organ, yet it shares qualities of both. Like an organism it possesses the quality of possessing unique DNA, like an organ it is part of a larger entity that regulates its metabolism. Again, there are no clear answers here.
More generally though, the last century and a half of medical technology have not provided the clear answers you seem to think they have. In fact, they've made this whole discussion kind of irrelevant. There is nothing special or distinctive about life to separate it from the rest of the universe. It follows the same physical laws. There is no soul hiding in the DNA strands, it's just meaningless strings of molecules, the same as all the other stuff in the universe.
Again, we arrive at the fundamental contradiction in your beliefs. You want there to be something sacred about life, yet you also want to boil life down to material phenomena that absolutely preclude that kind of sacredness. In historical Christianity, the thing you mock as "millennia old dogma" the person was the soul and the body was a mere vessel. This is, frankly, not as silly as you seem to think it is, it reflects the reality that there is a subjective quality to the state of being conscious that is not (yet) reducible to physics. Whether it's some literal soul or an emergent quality of the whole becoming greater than the sum of its parts, there is something mysterious and numinous about consciousness. Despite your insistence to the contrary, medical science has very little to say about that yet.
Again, if you want to live in a world where a clump of cells is the same as a thinking, feeling person, then fine. But by doing so you have reduced life to meaninglessness. You have openly admitted that what you think and what you believe and what you value means absolutely fucking nothing. You are no more important or sacred or special than any of the bacteria living in your gut.