Like the saying goes, "don't believe everything you read." There are other companies who manufacture this type of comb. I have had mine for well over ten years and never had any problem with the teeth falling out. Unfortunately many times, although not always, people only write about bad reviews or complaints and you don't hear about the positive ones.Reviews for the Greyhound comb you linked say:
"I ordered this comb strictly due to the confidence I had in the brand. I used greyhound combs when grooming professionally in the 80s and 90s. Recently started grooming again, this time as a hobby though. I had good experience with greyhound combs so didn’t hesitate to order one. When finishing a dog the first time I used it two teeth fell out. Very shocked and disappointed in the quality. I’m hoping it’s just an isolated event. Chewy was very quick to respond and I have absolutely no issues with them!"
"I bought this to do some grooming on my 6 month old Cockapoo. It arrived and two of the tines had already fallen out in the package. I tried to use it and each time I did more tines fell out. It is truly a cheaply and poorly made comb. I definitely do not recommend it. Chewey sells the Andis comb which is much better."