This is one of the most ridiculous claims I have ever seen.
First of all, there is not just one casein, caseins are a family of proteins.
Caseins are found in mammals milk in different proportion, generally quite high (that is why they are called caseins, from the Latin caseus, meaning cheese).
As the other answer points out, almost 50% of the protein content of human milk is made up of caseins during late lactation (from Human-milk proteins: analysis of casein and casein subunits by anion- exchange chromatography, gel electrophoresis, and specific staining methods.)
As for cow's milk:
Casein is the most important protein in bovine milk under both quantitative and nutritional aspects, as it represent approximately 80% of the total protein content (corresponding to 2.5–3%, w/v) and is rich in essential amino acids.
So, essentially Dr. Tombak claims that all the people around the world who drink milk and eat cheese are very lucky and have not be killed by it so far...
Anyway, to the specific claim:
Casein is a protein needed by the calf for building its hoofs and horns. ... Human beings do not have hoofs or horns. Why would they need so much casein?
This does not really make sense. Proteins are digested and broken up into aminoacids, which are always the same 21, no matter the source of the protein. The fact that casein is found in hoofs and horns is absolutely irrelevant: calfs synthesise it, they don't use it directly from the proteins found in their mother's milk.
Chapter 23.1.1 of Biochemistry. (5th ed.) by Berg et al. explains this process.
Protein digestion begins in the stomach, where the acidic environment favors protein denaturation. Denatured proteins are more accessible as substrates for proteolysis than are native proteins. The primary proteolytic enzyme of the stomach is pepsin, a nonspecific protease that, remarkably, is maximally active at pH 2. Thus, pepsin can be active in the highly acidic environment of the stomach, even though other proteins undergo denaturation there.
Protein degradation continues in the lumen of the intestine owing to the activity of proteolytic enzymes secreted by the pancreas. These proteins, introduced in Chapters 9 and 10 (Sections 9.1 and 10.5), are secreted as inactive zymogens and then converted into active enzymes. The battery of enzymes displays a wide array of specificity, and so the substrates are degraded into free amino acids as well as di- and tripeptides. Digestion is further enhanced by proteases, such as aminopeptidase N, that are located in the plasma membrane of the intestinal cells. Aminopeptidases digest proteins from the amino-terminal end. Single amino acids, as well as di- and tripeptides, are transported into the intestinal cells from the lumen and subsequently released into the blood for absorption by other tissues
Source: The Digestion and Absorption of Dietary Proteins
Finally, a remark on the author of the book, Mikhail Tombak, Ph.D.
I was wondering what subject his PhD was in, but couldn't really find much about it.
Now, of course I may just need to search some more, but the best I could find was a copied-and-pasted-across-multiple-sites (including Start Healthy Life) biography stating:
Mikhail Tombak, Ph.D. graduated from the faculty of biology and chemistry of the Russian University. For many years he was the head of Center for Health Sciences in Moscow;
Needless to say there is no "Russian University" (e.g.)... and I could not find any evidence of a Center for Health Sciences in Moscow either.
Actually, if you Google for "Center for Health Sciences, Moscow Mikhail Tombak", you will only fall onto reviews of his books... so, well probably I would not really trust the source of the claim.