Let me have some fun and maybe help you understand how the sex link thing works.
I assume you have a very basic understanding of genetics. Living animals, including chickens, generally have a pair of genes for each trait. When they reproduce, they give one of each pair to their offspring. There is no telling if they are going to give the left or right gene. Each time, it is random. It might be the left or the right. You never know for sure which it will be the next time.
With chickens, a lot of the genes are either “it is” or “it is not”. Either it is barred or it is not barred, for example. Or it is a mahogany or it is a not-mahogany. It is a pea comb or it is not a pea comb. There are exceptions like partial dominance or incomplete dominance, but I'm trying to keep this simple.
The end result of what a chicken looks lie depends not only if one specific gene is present or whether or not a different gene is present. For example, if barring is present and the chicken is black, you will be able to see the barring. If the chicken is white, the barring is still there but you can’t see it. Whether it is black or white has nothing to do with the barring gene, just whether you can see the barring if it is present.
The offspring gets one copy of each gene from its parents, one from the mother and one from the father. There is an exception to this which is how we make sex links, but I’ll get to that.
Some genes are dominant and some are recessive. For example, barring is dominant over not barred. If a chick gets a barred from its mother and a not-barred from its father, the chick will show barring if the other genes allow it to show. Silver is dominant over gold so if one of each is present you will see the silver, not the gold.
A rooster is generous to all his chicks. He gives one copy of each gene to every one of his offspring, male or female. If he has two not-barred genes, he is going to give a not-barred gene to each and every one of his offspring. If he has two barred genes, same thing. Every offspring gets a barred gene. But if he has one barred and one not barred, he might give a barred gene to an offspring or he might give a not barred. Being a generous soul, he will give each offspring a gene, you just don’t know which one it will be.
A hen, on the other hand, is a sexist. She is generous to her sons but stingy toward her daughters. She gladly gives a copy of each and every gene she has to all her sons. She gives her daughters copies of most of her genes, but certain ones she stingily withholds. The ones she withholds are certain specific genes each and every time. This is why the hen controls the sex of her offspring. If she gives a full set, she has a son. If she withholds some, she has a daughter. These genes are called the sex link genes.
If one of these sex-linked genes is dominant and causes something to show up on the hatched chick, you can tell the sex of the chick at hatch provided the parents are set up properly with the right genetics. Black sex links depend on the barring gene for this. The hen has only one copy of the barring gene. If it is barred, she is barred. If she has the not-barred gene, she is not barred. If she is barred, you know she will give the barred gene to her son and not to her daughter. The only gene the daughter gets comes from the father.
Remember that the barred gene is dominant over the not-barred gene. If the rooster has even one copy of the barred gene he will look barred. So if the rooster is not barred, he will give a not-barred gene to each or his offspring. His daughters will not be barred. But if the hen gives a barred gene to his son, that son will be barred. So if the other genes allow the barring to show in the down at hatch, you have a black sex link.
But notice that the children cannot be used for this. For this to work, the hen has to be barred. In a black sex link, the daughter is not barred. For this to work, the rooster has to be pure for not barred, but in a black sex link the son has one barred gene and one not barred gene.
The same exact thing can be set up with silver being dominant over gold. This is how you get red sex links. You can do the same thing with the slow feather gene being dominant over the slow feather gene. That’s how you can feather-sex if the parents are set up right.
I don’t know if this is any easier to understand than Tadkerson’s explanation. Once you get a grasp of the principles, it’s not that hard. But until you get that grasp it can be difficult.