I feel like the best way to understand this is for me to break down your argument to its various pieces.
What you're arguing is that DNA is what imparts humanity. To be more specific, your argument is that the formation of novel DNA is what makes a person. That step somehow imparts personhood, ergo one becomes a person when one's DNA finishes the process of homologous recombination and forms a zygote with this novel genome.
You provide 4 reasons for why this is true.
First, you argue that DNA is immutable. In a sense, you are correct: our DNA is largely maintained from the moment it finishes recombining in the zygote to the ends of our lives. However, it's that "largely" part that I take issue with. Our genomes are built with telomeres on the ends that get eaten away over the course of our lives, meaning that our genomes are getting shorter. DNA viruses will, in many cases, incorporate into the genomes of many cells in our bodies. If you stayed out in the sun too long, you could mutate a variety of genomes on your epidermis. So, your argument would have to morph: it's not that DNA as a whole has to remain the same, but some unknown number of core sequences must be maintained. And this is where we get into arbitrary selection. Why that specific number of sequences, why those sequences in particular, why ignore others, and if a human is born without even one of them, are they human?
Second, you argue that DNA underpins everything we are. This is an outdated view of how DNA works that assumes that DNA alone is responsible for everything we are. Setting aside issues of nature vs. nurture, there's a variety of molecular biological issues that affect how DNA is expressed and, thus, affect what we are. Epigenetics are probably the best known of the bunch, but if you want to get into it, I can tell you all about the various proteins, ligands, carbohydrates and all manner of other molecular signals that play a role in what we are. Why are they not worthy of this designation?
Third, you argue that DNA is the first step for a human. I've already pointed out that DNA doesn't exist in a vacuum, and therefore that arguing that it is the "first step" is a bit like arguing that flint is the first step in starting a fire. Flint is a part of the equation, it's required to get to the end point of making a fire, but it's far from the only thing required to make that fire happen, and if it's all you had, you'd be out of luck. For that matter, if we're concerned about what the first step in a human is, then this is an arbitrary choice. Looking back to my analogy, if we're really concerned about encompassing all that was responsible for the start of that fire, then we should consider how the flint was made. The flint didn't just pop into existence - this rock formed over time. If we truly wish to know the origins of the fire that we are trying to generate, then we should consider further back to the generation of that flint, the origins of the metal you strike it against, the generation of the tinder it lights, all of it. Why should we ever leave it to chance that we're excluding the essential element if our goal is to ensure that we leave no stone unturned, that we don't allow any persons to be denied their human rights? Benefit of the doubt should apply as far back as possible, should it not?
Fourth, you argue that it's uniqueness sets it apart. I'll ignore that there are other elements of us that also set us apart from others and just focus on DNA. Also, let's set aside the existence of twins and clones, both of which demonstrate instances where DNA is absolutely not unique. What, exactly, makes DNA unique? You would argue (quite rightly) that it's not the sperm or the ovum individually. What makes it unique is the process of homologous recombination, where the DNA of the two gametes is split up and shared. So, then, it's not the DNA that actually makes us unique, but rather the process of homologous recombination, right? We are persons because this process occurred. I suppose you could argue that, so long as there is unique DNA in a cell, it doesn't so much matter how it's achieved. In doing so, though, you leave the door open to any number of means by which DNA could be modified in any number of cells. I could irradiate cells and produce a unique DNA sequence. Have I created new life? You might argue that that life needs to have a potential to become an adult, so fine: if I irradiate sperm cells, I should be creating new life as well, since those sequences would now be unique and could go on to fertilize an ovum. Also, if I somehow modify the genomes of any stage post-zygote (this is not science fiction - it has been done), then by that same logic, I must be making new life at a later stage than the zygote. In other words, if I use your logic that it's the uniqueness of the DNA that decides when a life begins, then that is non-unique to the zygote.
I'm really trying to set each of these points apart and examine them individually. Maybe I'm missing something, and if so we can most certainly go back and address it. I do, however, have one last thing to add.
You are almost certainly going to have a problem with my argument that your perspective is a personal whim, so I'll address that. The fact that you have support for your position doesn't make it any less of a personal whim. You're assuming the consequent by defining a specific set of criteria for what you believe makes a person, and then saying that DNA meets that criteria via a, b, and c. Just because you explained how it meets those criteria doesn't mean that the criteria themselves are any less the result of your personal whims. I am certain that you will argue that the criteria you set are objective, but as I've pointed out several times already, those criteria are based in your slanted view of what you want to be a person. You've designed those criteria to exclude all other factors (though I don't think they actually do), and then proclaimed that, by fulfilling them, you've proven your point. I don't see you having justified your criteria in a way that's objective. Each of your justifications is arbitrary. Coming first doesn't make it the appropriate place to insert personhood. Something having the quality of being immutable doesn't mean that it imparts the immutability of personhood. Having a role to play in how we develop doesn't make it the factor that imparts personhood. And its being unique only provides a distinguishing factor from one individual from another, not the obvious label of personhood. All these points do is beg the question: why do they (and nothing else) impart personhood? Why can't they just be a part of what makes a person, and other factors complete said person? Or, if just one of these factors is absent from a human, why should or shouldn't we consider them a person? You can argue that this is all objective, but there are clearly some strong assumptions baked into your argument. Those are the personal whims that I've referred to, and the main reasons why I'm finding it so hard to agree with you.