There is a longer answer, but it's thrashed back and forth so often I really don't care. As a rule, though, people who argue that female Space Marines are appropriate and plausible in the background tend not to be taken seriously. Cool models, no one has a problem with, but no one believes female Marines are plausible. I am, of course, not a biologist, but I'm afraid it is stated that the process which creates a Marine is male-exclusive.
These considerations mean that only a small proportion of people can become Space Marines. They must be male because zygotes are keyed to male hormones and tissue types, hence the need for tissue compatibility tests and psychological screening. If these tests prove successful, a candidate becomes a neophyte.
Incidentally, I wouldn't consider notions of political correctness to be at all relevant to this discussion. No comment on the other qualities of women or men is intended; merely that only men can become Marines.
Women have "male hormones", just in smaller quantities. And there is no difference in tissue types between the genders. (Even the obvious, the Testes, is the same tissue _type_ as ovaries. Type is pretty general.) I should note that I find it pretty unlikely that the geneseed is somehow keyed to the Testes, but transexuals do exist and have the requisite part as well as possibly female physiology - one could certainly look like a woman in a space marine suit.
Psychological compatibility is pretty trivial. Gender is not the same as sex, and gender is pretty fluid. Regardless of what 'personality' (hormone balance?) the geneseed requires, there are going to be some women who are matches - possibly just fewer than the total number of male matches. We're talking about long tails of distributions here with different means, not exclusive sets.
Actually, the argument that the geneseed cannot join with the female gene is plausible. Why? Because men also have a Y chromosome. If the geneseed needs to join with a Y chromosome in order to work, or the use of testosterone, there cannot be any female marines. You kinda left that out. Its like saying that men can give birth, because we also have an X chromosome, which is required to form the female genitalia, and therefore, if we try hard enough, we should be able to form those, and eventually give birth.
Basically, you're only looking at half of the answer, and building your argument from there, ignoring the part that makes the explanation viable.
XXY is generally considered "female" (and many are indistinguishable appearance-wise), but has a Y chromosome.
Women have testosterone.
Not all women can give birth. Having an X chromosome is insufficient for doing so. In fact, Turner's syndrome (XO, no second sex chromosome) are female but sterile. So clearly 2 Xs is required for giving birth. The point was that possession of an X can't disqualify one from something, because men also have an X. There is no exclusively female chromosome (or even gene), only an exclusively male chromosome (and genes). And most of that is just a truncated X - there are very few unique genes on it, and virtually all have to do with sex organ differentiation.
You can get women to form a penis and testes by increasing the testosterones levels in their system during development. Similarly, by increasing estrogen during male development you can stop or arrest the development of the penis and cause the development of breasts and (if early enough) a birth canal et al. They both have the necessary genes for it - its gene/hormone interactions which cause gender differences, not just genes keyed for it.
Sex and gender are a lot more plastic than people like to think, and there are lots of weird cases in terms of aberrent chromosome numbers (XO, XXY, XYY, XXX) which play havoc with our standard notions of sex and gender. And the physical biology is the easy part. I am pretty confident that for any plausible reason you can give why women are incapable of being space marines, I can find a case that is a "woman" by colloquial english usage and gross physiological criteria and would qualify.
Remember also that the Space Marine fluff is written "in character", by which i mean from the perspective of someone in the space marine universe. It may be what they believe. A lot of it sounds like gobbledygook and has nothing to do with real biology. (Male hormones being implied to be exclusive to males?) It might explain why more chapters don't do it, or it might have been written by someone with an agenda to insure an all-male space marine system. Since it is written in-character, it means its as fallible as a character in the universe (notably, its unnamed and presumably unknown author), and subject to all the biases its author had. Similarly, people in reality at one point claimed that light couldn't travel through a vacuum, there had to be some medium through which it traveled. They were wrong, but it was the accepted wisdom of their day. Similarly, the Rites of Initiation could be wrong, either unintentionally or trying purposefully to be misleading. Especially in an age where technology is poorly understood and the words and devices of their forbearers taken as holy gospel, that there is wrong science and explanation embedded in it that goes undetected would not even be remarkable. (That none of the GW writers are scientists, or even apparently took a basic biology class in college from the looks of that Rites of Initiation quote, makes this a good thing - they don't have to worry about saying something that could actually be possible.)