A human embryo is alive and contains the full capability of progressing into a full grown adult. The embryo is not a part of the mother’s body— they have different DNA than the mother. The only coherent definition of when life begins that can be found is at fertilization because all others are arbitrary. If you say that life begins at birth, then the fetus just about to be born is not a person until it comes out, even though it’s structure before and after that point are essentially identical. The same can be said of any other arbitrary point along fetal development, such as viability or when a heart rate is detected, etc. The only logical place to assign the beginning of a life to is to fertilization (or perhaps implantation but that doesn’t make as much sense since the zygote is still around before then). If you try to trace a person’s existence backward, the place where the existence begins is at fertilization. Before then, the individual person is an egg and a sperm, clearly neither component is a person (and only has half the DNA). As far as truly proving it’s a person, you can’t prove anyone is a person. I can’t prove you are a person and you can’t prove I am.
You need to read up on reproductive physiology. For one, it is absolutely untrue that all zygotes contain "the full capability of progressing into a full grown adult". All zygotes with trisomies other than Trisomy-21 have a 0% chance of progressing into a full grown adult. Zygotes with Tay Sachs have a 0% chance of progressing into a full grown adult. Zygotes with any number of inherent diseases have a 0% chance of progressing into a full grown adult. In fact, many, many disorders mean it isn't even possible for a zygote to develop into a fetus, let alone a full grown adult, and many proto-humans with what we would consider perfectly well-formed genomes are spontaneously aborted all the time; though we wouldn't know it otherwise, they apparently had a 0% chance of progressing into a full grown adult. (Note that this isn't a particularly good justification for abortion in those cases, either, as we'd then have to be okay with infanticide in, say, cases of Tay-Sachs. I'm just saying that your first definition needs revision.)
Second, and much more importantly, you're absolutely wrong that "the only logical place to assign the beginning of a life to is fertilization", because there is no moment wherein suddenly "fertilization" happens. It's a process, and it takes place over time. First the sperm has to encounter the egg, then it has to merge with the egg, then the
DNA of the sperm and the egg have to meet up and combine together, then that DNA needs to be replicated before it reaches the usual human contingent of 46 chromosomes (or, not-46 chromosomes, as the case may be), then it needs to replicate
again to start dividing. My recollection is that this process takes about 48 hours, total; after the zygote zooms down the Fallopian tube, it still needs to implant in the uterus. At what point does "fertilization" occur? I don't see any good dividing line here; perhaps you'd propose the 46-chromosome point (as you say, there's something special about DNA combining together), but, even then, it is every bit a part of a continuum as, say, birth is.
And, of course, you have to consider what happens next. Let's say the cell is merrily dividing, and suddenly a division happens a bit too divisively and... voila! Identical twins. At what point did each twin's life begin? Did they both start at conception and happened to share a body? (If so, should we charge fertility specialists who destroy embryos before they divide very much with just one murder, or should we charge them with more just in case?) Did the life of one start at conception and the other start when they split apart? Did they
both start when the split apart? (If either of the latter two, why is fertilization so important, then, if there's a bifurcated system in which twins start later than singletons?)
Look, I don't mean to belittle your beliefs; I think "when life begins" is a problem that
cannot be answered scientifically. You can define it however you think is appropriate. But I just want to make sure you know that, just as there's no scientific case for life to begin at birth, there's also none for life to begin at conception/fertilization/implantation or whatever you want to call it when the sperm meets the egg and does something-or-other. There's nothing more "natural" or "abrupt" or "logical" about "fertilization" as a thing than there is about "birth" as a thing.
