Throw your mind initially to the moment of conception. It is empirically undeniable that one sperm joins with one egg, in all species (not just those presumed to have souls), to form one cell with a complete genome. This cell then splits over a period of time - in humans, typically 9 months - until eventually, a young child is born (or hatches from an egg, whichever method the species uses). But sometimes things go wrong - the clump of cells, still very early in the process of maturing to an independent collection of cells, splits into two. If this happens too late, a miscarriage results. Yet if it happens earlier, the result is one (usually) rejoiced in. Identical twins.
Let us move now though to the time even before conception. In the man, the sperm is produced by the same process of cellular division that usually occurs in the body and that is in fact the process by which a fetus matures into an infant. The time at which a female human body gains its eggs is a somewhat murkier area, but it is again empirically undeniable that this happens after conception. (To argue it happens before conception is ridiculous, and dooms any proponent of such a theory to an infinite regress of Russian Matryoshka dolls).
Before moving on, I will now note that I take it as a given that you accept the claims made above. Of course, there will be some who do not, just as there are some who still believe in a flat earth. To you I can only say: go jump off the edge. Your fantasies are pointless self-imposed obstacles, and at some point reality is going to club you to (literally) death.
But assume you do agree with the quick summary of reproductive biology as it manifests itself on Earth - yet still believe in a soul. You have some impossible questions to answer.
The first of these is simple - when does the soul appear? Does it appear at the moment of fertilisation? Or is there one in every sperm, and every egg, or one in every sperm or one in every egg? Or does it appear at some point during growth? At birth?
It would initially seem the most likely time for a soul to just magically appear is of course the moment the egg is fertilised by the sperm - the moment of conception. Yet really - why here and why now? What's so special about the joining of two small bits of (mostly) carbon and hydrogen? What's so special about these two chunks of DNA? The cells are after all, everyone agrees, not alive in the same way a person is - the cells in your body die all the time, and even your brain cells do, at a rate of at least one every 3 minutes - yet you do not die with them. But return to the sperm and the egg. First there were two cells. Now there is one - no more humanly alive than the original two. How can this subtraction result in addition? Oh sure - the egg now has a complete genome. But so does every other cell in the body, excluding of course the currently unused eggs (and sperm, in the man). Is it that every distinct genome gets one soul? Of course, such a conclusion must account for the proliferation of souls that would occur in every living human, as the genome in our various cells mutates and decays (due to telomere decay - it is this mutation that can cause cancer) as we age. Clearly, concluding that it is the moment of fertilisation that results in the creation of the soul brings with it too many arbitrary answers and empty or unanswered questions. Such a conclusion is inescapably ontologically messy and self-contradictory.
On the other hand, perhaps there is one in every cell - one per sperm and one per egg. Yet we still have all the problems of “when and where”, as outlined above, and all the problems of twinning too (discussed below), as these cells produce through the same process of philosophical fission as identical twins. Worse than these philosophical problems though, presumably killing a soul is bad? Then masturbation is horrifically evil, as Christian fundamentalists have proclaimed for eons. But so is conception. Sure, one sperm survives - but 3 to 4 hundred million others die. That's a lot of death for one life. Even worse, simply existing is evil, because in the male body, sperm are recycled regularly if they do not get used up (wasted?) - and with them go their souls, surely.
The same problem exists if souls begin only in eggs. After all, simply ovulating without becoming pregnant condemns that soul to death. Worse, a women will have far more eggs - roughly 400 - than can be used, even if she were constantly pregnant. Thus she is in no better position than the man. Oh sure, numerically she will kill less - but a murderer is not excused by murdering fewer. Then again, maybe it's not wrong to kill a soul unless it is in a grown body? So we come to the question of abortion. After all, how grown is grown enough? There must be some definable point at which abortion is no longer OK - and the idea that there is a time until which it is OK is a position many may find uncomfortable. Yet such a point in time is surely arbitrary? Say that it occurs when your brain (or heart, or body) has i cells, but not i-1. How can this extra one cell account for the difference between posessing a soul and being soulless? Clearly, no matter how you cut the pie, a soul is at best, a trivial thing, unimportant and dependent on the most slight change.
Yet there is still the second problem. This is of course: what happens in the case of identical twinning? Even if we can answer the question regarding when the soul first appears, such twins still give us a problem. Does each have a soul? Is it a whole soul? If so, where did this extra soul come from, and who gets the original - or does that one die? Or does each have just a half soul? Or were there two all along? Are there any people who were meant to be identical twins, but aren't, and so have two souls? Is murdering them worse than murdering someone with only one? If so, how can we tell who these people are, and why is it worse? I could go on, but I'm sure you can see the nightmare you'll find yourself in if you hold to souls. I agree, it would be nice, fantastic in fact, if there were and could be souls. It would make things so much easier, just like if there was a God. But there cannot be, and clinging to a sinking ship will not make things easier for you.
Thus we must draw the conclusion: based on the undeniable empirical evidence, the existence of souls must simply be answered in the negative. Concluding otherwise creates a horrifically messy ontological world, full of self-contradictions and arbitrary, unexplainable answers - “goddidit”.