White boxers aren't "bad". As pets, companions, working and service dogs, they are every bit as good as their coloured counterparts, and should be viewed as such.
However, in terms of the boxer standard, showing
and breeding, they are and always will be disqualified. There are GOOD reasons for this - it's not that someone just didn't like whites.
White boxers have a double dose of a gene known as the extreme white spotting allele. As a result of that gene, a high proportion of white boxers are bilaterally or unilaterally deaf. The problem is that the gene suppresses the development of pigment (that's why the dog is white). White is not a colour, in fact, but lack of pigment. No problem with that when it's only coat colour you're talking about - but is ISN'T just coat colour. It is sensory organs, including the ears. Pigment is related to the ability to hear. That is,
lack of pigment cells (melanocytes) in the inner ear causes the cells supporting the fine hairs required for hearing to die. No hair cells means no hair. And no hair means no ability to hear. Hence, deafness. It is thought that about 20% of white boxers are deaf, versus under 2% of coloured. So you can start to see the scale we're talking about here.
Now whilst deafness isn't the end of the world, and there are plenty of deaf dogs around that make perfectly wonderful pets... the reality of this world is that there AREN'T as many wonderful owners willing to give deaf dogs homes. With a defect like that, a great many end up in shelters and euthanised. And this will remain the case until such time as human society continues to have a pet overpopulation problem, and more people are willing to take on deaf pets.
So, it doesn't take a great deal of thought to understand that it is not a responsible breeding practice to deliberately breed animals that have a high risk of producing deaf offspring. And that's the problem with breeding whites. Note that it's not a matter of whether or not they're born - but what would happen to the incidence of deafness throughout the breed if they were used for breeding - as they'd cause (further) pigment dilution throughout the breed. And the answer (backed by canine geneticists) is that the breed-wide deafness rate would rocket upward from its current low level (circa 1.5% in coloured dogs) toward the 15-20% levels seen in whites. Which in turn risks a massive increase in the abandonment/euthanasia rate. Not what anyone wants, I would say.
Therefore, white boxers, although every bit as good pets as coloured dogs, must not ever be used for breeding. Not under any circumstances.
Put more strongly, there is absolutely no excuse for deliberately breeding a genetic defect into a dog breed. Just as there is no excuse for deliberately breeding an animal that suffers a genetically inheritable heart defect (for example), there is no excuse for anyone breeding an animal that is likely to produce deaf offspring AND continue the problem for generations to come.
And that is what brings us to showing, and the breed standard. There is actually only one purpose to the show ring: to select specimens that (subject to health screening) are suitable for breeding. That's it. There is
no other reason.
And logically from that, the only animals eligible to compete are those capable of being bred. You cannot, for example, show a spayed/neutered animal - there is no point. And this is why whites are ineligible for showing. They are not, under any circumstances, suitable for breeding. Therefore, they are excluded from the breeding selection panel that is the show ring.
Does that make some sense to you? It is NOT discriminatory, in the sense that someone (or even many people) don't like them, want to exclude them, or wipe them out. It is purely about the fact that they're not for breeding - and showing exists solely for the purpose of selecting animals for breeding. And of course, the last link in the chain is the breed standard

That is the blueprint against which breeding-
prospect animals are to be judged. In order to be a breeding prospect, the animal needs to be intact (not spayed/neutered), and
not white.
Show regulations take care of the intact bit (which, naturally, is common to
every dog breed)... the individual breed standards take care of exclusionary factors specific to the breed in question. In the case of boxers, that is white coat colour (because of the genes that cause it in this breed).