I’m not sure that this has a factual answer but I’ll start it here.
Dogs are fairly universally loved and valued by society big calling someone a dog is supposedly insulting. I believe that it is even more insulting in Muslim cultures. Is there a reasonable or logical reason for it? Calling someone a cat would be confusing and AFAICT, is not done in English speaking countries.
Why dogs?
Because being called a non-human animal is–um–dehumanizing them?
If you are asking why, in Islam, dogs are considered unclean while cats are OK,
it’s hard to give a factual answer, though cats are often visible fastidiously cleaning themselves so this might have something to do with it.
Here is an interesting article I just found on thise dog-gone Muslim attitudes:
Human females are often described as feline or cat-like or catty or similar, and I don’t think it’s meant as a compliment.
Diogenes of Sinope certainly wasn’t offended at being called a dog, and I wouldn’t be either, nor should anyone else called a dog by me.
On the other hand, if you are hip, then being called a cat is good.
It’s somewhat similar to calling somebody a child. Children themselves are generally highly regarded. But an adult who is equated to a child is being seen as less than a full adult.
This goes way back. dogs were not companions back then but workers/slaves of their masters.
Like the Quran the Bible doesn’t have great things to say about dogs, and have used the dog as a unworthy human:
Rev 22:14 “Blessed are those who wash their robes, that they may have the right to the tree of life and may go through the gates into the city.15 Outside are the dogs , those who practice magic arts, the sexually immoral, the murderers, the idolaters and everyone who loves and practices falsehood.
(Or just dogs just can’t get into heaven by design)
More famous is the story of the Caanite woman who rebuked Jesus (and won) in Matt 15:
26 He (Jesus) replied, “It is not right to take the children’s bread and toss it to the dogs.”
27 “Yes it is, Lord,” she said. “Even the dogs eat the crumbs that fall from their master’s table.”
Also while dog is not mentioned by name, In the book of Ruth of the Bible, Ruth starts out a very low member of society, and has a very dog like action sleeping at the feet of the land owner Boaz.
In English, the insult goes back at least as far as Shakespeare, with a bit of “yo mama” thrown in;
I would have thought that anyone who has owned a dog, other than a pampered pooch, will know that dogs are amoral, lazy, uncaring of personal hygiene and have disgusting ideas about what is good to eat.
Cats don’t get off scot-free. “Catty comments” are deliberately hurtful and/or spiteful remarks.
Provided it’s the 1950s and you’re a hip beatnik. 
On the other hand “Oh, you dog!” Is admiringly applied to men perceived as successful with women.
But a woman calling a man a dog is not typically seen as a sign of admiration.
This is what I was going to say. Or you could say “you sly dog” to someone who gets away with a minor indiscretion.
Some want to be a dog.
IIRC, David, speaking to Saul and trying to assuage his jealousy, refers to himself self-deprecatingly as a “dead dog”.
If I had to guess, I would speculate that it may be a combination of dogs 1) mingling with humans, and 2) eating feces.
George Carlin on dogs:
"Dog is lying out there in the living room, you got all these people sitting around, you got a little chip, a little dip. Dog’s in full view of everyone, got carrot sticks, celery sticks, little lady fingers, finger ladies, all sorts of little things that you got. And everybody’s eating nicely, and you look down and you realize that the dog is licking his balls. No one says anything, no one mentions it, spectacular thing going on. Hey, if I could reach, I’d never leave the house. "
Ok:
Man visits mate with dog. They sit drinking beer and eating crisps. The dog sits licking his balls.
Man: “I wish I could do that.”
Mate: “Give him a crisp and he’ll let you.”
Calling someone a “dog” is basically saying that they’re unable or unwilling to control their “base” appetites. Dogs don’t really do temperance. They’ll eat 'til they get sick, then eat the sick. They’ll fuck under absolutely any circumstance, regardless if it’s appropriate at that time, or with that person. And while famously loyal, their loyalty is indiscriminate, and not based on the worth or station of their master - a dog will be just as devoted a servant to an itinerate drunkard as they are to a reigning monarch.
So, basically, calling someone a dog is saying that they lack temperance and propriety, and that their nature is essentially subservient.
I think the same moral dilemmas can be applied to dogs’ behaviors as to humans’, including ideas of laziness.