There are two sources. If it were down to 'options' 1000 and 1001 and 0001 and 1010 would mean binary isn't binary. The two sources are X and Y chromosomes and male an female anatomies, just as in maths the two sources are 0 and 1
You might like to think how a combination of 0 and 1 is binary but a combination of X Y or a combination of male and female isnt?
I'll post it here, too, in hopes that you might actually read and understand at least one of them.
You don't seem to understand what binary notation is. 10101 isn't a binary number; it's a number expressed in binary notation
. You can express it any number of other ways.
That does not mean that all binary numbers are binary; they can't be, since there are an infinite number of them. It just means that they are all composed of binary digits when expressed in binary notation
. In octal that number is 25; in decimal (which we are used to) it's 21; in hex it's 15. All of those are just ways of expressing the same number. The number doesn't become binary when you express it as 10101; binary is just a method of expressing the number. It doesn't become a hexidecimal number when it's written 15; it's the same number.
That's why you hear questions like "That number - what is it in hex?" from programmers. They know it's the same number no matter how you express it; they just want it (in this instance) expressed in hexidecimal because that's how it is expressed in the particular thing they are looking at.
We commonly talk of 'binary numbers' and 'decimal numbers' and 'hex numbers' for short; nobody (but you, apparently) thinks the numbers are actually binary, or decimal, or hexidecimal. The method of expressing them is; the numbers are not.
Binary always has only two possibilities. That's what binary means
. If there are three possibilities, or four, or 1, or zero, then it's not binary. Again, that's just what the word means
. Like binary numbers, sex chromosomes are commonly expressed in a particular binary notation - using X and Y as the symbols, rather than 1 and 0 (incidentally, I've seen binary notation also use Y and N instead of 1 and 0 - the symbols themselves don't matter).
But as soon as the possible values expressed by the notation become more than two, then those values are not binary. The notation is; the value is not. XX is a different value than XY, and as long as we stop there, it's true that the possible values are binary. In this case, both the symbols and the values are binary. But as soon as we agree that XXY is a valid combination, the possible values stop being binary; there are three of them. The symbols remain binary (there are only two) but the values those symbols can express do not
That is why the fact that only X and Y are used to express the values of sex chromosomes does not make sex binary. It makes the notation
in which they are expressed binary. It does not make the possible values binary; they are not. This is what has been repeatedly stated to you. As soon as you admit a possible arrangement other than XX and XY, you admit that the choices are not binary, even though the symbols are. That is why your admission that there is female (XX), male (XY) and various other mixes of both (XXY, etc.) is an admission that sex is not binary, although the notation remains binary. Which is why it is valid for me to say that you have admitted that sex is not binary (you just don't know what 'binary' means), and it is not valid for you to say that I have admitted that sex is binary.
No doubt you'll simply ignore this and post some dismissive one-liner. But it's here so you cannot complain that your repeated error has not been explained.