That’s because domesticated dogs are stupid. Well, most of them, at least.
Actually, skunks are a bit more distant than that. Under the revised classification, the Procyonidae (raccoons) are the sister group to the Mustelidae; the Mephitidae is the sister group of the Mustelidae+Procyonidae clade. So if you wanted to have Mephitidae be a subfamily of Mustelidae, then you have to have Procyonidae as another subfamily.
Or highly poisonous Amazonian frogs being brightly colored.
Kung-Fu Panda anyone? 
As to skunks and evolution, I personally saw this in action years ago when my future wife and I were living on a suburban farm. There were two farm dogs that had counter-evolved to kill and eat skunks: the skunks would spray them, but the dogs ***simply didn’t care. ***
Great Horned Owls are one of the few (perhaps the only) predators to regularly take skunks. Like most birds, they have a poorly developed sense of smell, which may make them relatively immune to the skunk’s deterrent.
May? May? I’d venture that it definitely makes them immune!
Do other big birds of prey not take skunks as much? Why do the Great Horned get singled out as a major predator? I understand that skunks are mostly nocturnal, so hawks wouldn’t encounter them often, but aren’t there other large owl species that have the same range?
The Great Horned Owl is the largest owl in North America by weight. (The Great Gray Owl is longer but not as massive.) I doubt that the other North American owls are big enough to take a full grown skunk under most circumstances. Hawks sometimes prey on skunks, as you say don’t have the opportunity as often as owls.
Even so, a great horned owl that takes on a skunk is still going to end up stinking to everything else, which would probably make it harder for them to take other prey. So you would expect that the owls that instinctively avoid black-and-white-stripes would still have an advantage over the ones that don’t.
Well, first, the owl is attacking from above, and may not be within sniffing range of the prey until it’s too late. Second, even if the prey smells it, it’s likely to be thinking “skunk,” not owl. Since skunks are not particularly dangerous to most other animals preyed on by owls, this could actually end up being a kind of camouflage. Third, given that skunks are fairly large, common, slow-moving, clumsy, unwary, and not preyed on by most other predators, it makes them a very attractive prey item to any predator that isn’t deterred by the smell itself.
Note that dogs and other predators love to roll around in dung, carrion, and other smelly stuff in order to mask their own odor. It’s not being stinky that alarms a prey animal; it’s the smell of the predator.
Because I’m a weirdo I consider how the skunk’s spray evolved. Yep really. Oh my this bothers me because I’m taught every specialty mechanism of a living creature evolved by a random mutation. So I have to wonder how many different substances had to evolve and fail before that wonderful stinky musk came along. First maybe it was a mucus liquid (fail), urine? (fail), Windex? (fail), perfume? (fail)…wow we’re wasting millions of years aren’t we? But finally, Bingo! Stinky stuff! Oh yeah and there must be a way to propel it so to squirt the attacker… and that had to evolve also by random mutation at the same time.
Of course it happened that way. What’s the alternative? Yep, trust me, I’m educated.
You are assuming that evolution is directed, and that it’s “trying” to make a stinky smell. Not so. All the intermediate steps were successful in their own way, and none can be considered failures. Each one either conferred some advantage, or was not a disadvantage.
And this is a zombie thread.
I once saw a documentary about skunks and almost everyone who knew them claimed they were very friendly kind animals and only resorted to spraying if they feared for their lives.
Many of the people in this documentary had some skunks for pets and claimed they were just the best pets they ever had and they were extremely friendly and fun to have and that they never ever sprayed anyone.
It was a very interesting documentary. It made the point very clearly that de-scenting a skunk is much like de-clawing a cat and should never, ever be done. It is extremely cruel to do that as it will leave the skunk defenseless and if the skunk is ever returned to the wild, it will be very likely killed rather quickly without its defenses.
Since dogs have a sense of smell that is hundreds of times more sensitive than humans, it must really punish a dog to get sprayed. They probably regret it for a long long time. It must be extremely painful for them and since they can’t smell very well after getting sprayed, getting sprayed probably destroys much of their social abilitites for many days.
Your image of how evolution works is completely wrong, so you evidently haven’t been well educated scientifically. Substances wouldn’t have been generated by “random mutation” and then fail. Instead, a useful substance already present in the skunks’ ancestors was probably gradually converted into a defensive weapon.
Many mammals communicate with others of their species by scent. In particular, many of the skunks’ relatives such as polecats use fairly pungent smells secreted by their anal glands to indicate their identities to others of their species, mark territory, and attract mates. In skunks this already-existent system has been modified by making the secretion particularly offensive, and the anal glands more muscular so they can shoot the liquid as a spray. The changes were accomplished in a series of small steps. At each step the system was useful, but it gradually became more effective with each one.
Stinkybrains!
IMHO, if you own a domesticated skunk, cat, or dog, and your solution to not wanting it anymore is to dump it in the woods, then that is way more cruel than declawing etc. I heard/or I imagine that descenting is mandatory in many jurisdictions.
Hmm… have you ever seen a dog happily roll in garbage, shit, vomit, or any other stinky substances? (But I know, skunk spray might be aversive, stinking being its point.
There are many different ways that a skunk may be returned to the wild.
It need not be dumped. It could somehow escape it’s environment and run off into the wild.
Or it may be scared by some loud noise or some animal or other event and run off again into the wild.
In any case, I still believe it is very wrong to de-scent a skunk. Better not to take one as a pet if you plan on doing that.
And it’s just my opinion but I feel the same way about de-clawing a cat. You may choose to de-scent and de-claw your pets. I guess there is nothing to prevent you.
But I would never want to do that.
So, good luck to you and to your opinions. But I feel very sorry for any pets that are ever de-scented or de-clawed.
?? What is a polecat? I always thought that was just a colloquial synonym for skunk. It’s something different?
A skunk sat on a stump.
The stump thunk the skunk stunk.
The skunk thunk the stump stunk.
The polecat is the wild, non domesticated version of the ferret. There are fancy skunk breeds, but I don’t think this counts as real domestication.
Like most words in the English language, “polecat” has multiple meanings. It can refer to a skunk, as Senegoid says, or to the wild ancestor of the domestic ferret, as Dave_Enn says. (It’s also the name of several related species.) The “skunk” usage is largely confined to the US, or some areas thereof. Skunks aren’t native to Europe so over here “polecat” always means the ferret-like animal.
One of my dogs killed three skunks last spring and summer. 
I have a large fenced yard adjacent to woods. Skunks don’t run very fast and nor are they particularly speedy climbers, so if there’s one in my yard when I let the dogs out for a night-time pee, it doesn’t have much of a chance.
The dog didn’t appear the least bit distressed; in fact he seemed quite pleased with himself. So clearly not an aversive, at least not for him.
I don’t agree. Skunks very rarely actually spray an attacker - they very rarely have to. The fact that they are a skunk is usually good enough, in the wild, to ensure their immunity from attack. The predator sees what they are and steers clear (hence the warning pattern of their fur). A scentless skunk would benefit from the fact that every other skunk isn’t scentless. They would only be at risk from your typical brainless dog, the kind that often gets sprayed and pierced with porcupine quills.