For those of you coming from outside the very insular dog show/sport world health testing refers to preforming a variety of blood tests (DNA and other), x-rays, and exams to determine both a dog's current health and their propensity to develop disease in the future. Every breed has its list of breed specific problems and thus have their own set of health checks they should perform before breeding. This is in addition to routine pregnancy checkups on the mother and puppy vaccines, deepening, and vet checks.
For those of you experienced in more common breeds, it might sound odd, but I routinely see some form of the following argument in rare breed: "But my breed: ___, is prone to very few issues, so I don't need to health test" or "The people in my breed that do health test are really misrepresenting themselves because the diseases the dogs are prone to some have a test for them".
Let's address those separately.
In regard to the first statement, there are a number of rare breeds that really are quite healthy compared to the general population of dogs at large. That doesn't me that we as breeders can't still seek to improve on their breed's overall health.
Additionally, some rare breed have a very small gene pool. With any small gene pool you're going to start to run into problems with recessive diseases and keeping your coefficient of incest (link to explanation) thus helping maintain genetic diversity within your gene pool. In cases such as these utilizing genetic testing to ensure that your dogs really are clear of the widest array of diseases possible will be helpful. Additionally, it's going to help breeders identify carriers of diseases. It is becoming thought of as best practice not to completely eliminate carriers of non-lethal diseases from your gene pool but in order to maintain diversity instead breed carriers to clear dogs to decreases instances in the entire population. https://puredogtalk.com/bill-shelton-chapter-3-bottlenecks-marketing-adaptability-pure-dog-talk/
The second statement operates on a couple faulty assumptions:
First assumption is that breeders are only healthy testing as a selling point to sell more puppies while disengeniously advertising them as completely health guaranteed. I can tell you that I health test for myself first and foremost. Genetic testing is going to inform me as an owner whether I can expect my dog to remain healthy or not. For my dogs that are heavily into sports, x-rays of hips and elbows inform me whether my dogs have healthy enough joints to play those sports. I do health and genetic testing on my pet dogs too because I want to know what to expect, I just don't register them with the OFA because I don't need public accessibility on my italian getting) chihuahua mix.
That leads to the second assumption- that there's no need to health test because it's not testing for the breed specific diseases. To this I'll say that there are very few (with notable exceptions, azawakh not being one of them) rare breed populations that have extensive studies done on their DNA and breed populations. Recessive diseases can hide for many generations. Without widespread data and routine genetic testing the truth is we just don't know what diseases might be hiding in our breeds waiting to emerge. Additionally with azawakh, it's entirely possible that diseases that are common in country of origin we know nothing about because natural selection has ensured those dogs never reproduced, and yet carriers remain. Diseases that we might never expect could pop up without testing. By making (at the least) genetic testing routine, we'll have a good deal more information about the breed population at large available.