I think some of what's being discussed here is the difference between a stable, and an unstable, dog. From what I see around, there are a lot of unstable dogs out there now. I'm not sure people always even realize it OR know how to deal with it. In some cases, they even encourage it!
I had an encounter with someone like this recently. Two dogs, completely unstable, let off-leash at a dog park and immediately started attacking a young dog. Not only did the owner do nothing to stop it, she reinforced (rewarded) the behavior by patting them when they came back to her! I was stunned!! Furthermore, the owner of the dog who was attacked said it was "Ok". Wth?? Attacked dog, less than a year old, was cowering in the corner with its tail between its legs! Not ok!! That dog was clearly traumatized. (It happened several times.)
The trend seems to be people carrying dogs around with them or bringing them everywhere (I've seen quite a few in shopping carts in retail stores lately which were not service dogs) and treating them inappropriately, reinforcing bad behaviors (whether inadvertent or not) and letting their dogs run the show.
This is my opinion. I get where pp's are coming from when they're talking about how dogs see the world and that they elevate themselves when they're allowed on the sofa. But it's not the whole story. First, you need to have a stable dog, because an unstable dog can be dangerous in any circumstance - and you never know when it will happen. People also need to realize that when dogs are afraid they should NOT be patting them, they should just be leading the way to show the dog that there is nothing to be afraid OF. Act happy, encourage the dog to keep going, etc. But DON'T CODDLE. I know a dog who can't ride in the car because, as a puppy, he was coddled every time he showed fear when he got in the car, instead of just acting like all was ok. The lengths the family has to go to to get him to ride in the car is unbelievable. Do your dogs a favor and don't coddle them.
A stable dog who is INVITED on the sofa understands that if the person wants the dog off, the dog gets off, no problem. An unstable dog, otoh, may bite if you try to get them off the sofa. In fact, my last bite was from one of these unstable dogs. A friend had brought him over and he went up on my sofa. I non-chalantly went to take him off by the collar, which was a natural move for me (as he was NOT invited to go up on there), and he bit me. Turns out he was wearing a shock collar, and he had sensitivity of the neck. My hand was sore, but I felt so sorry for this dog. His people had made him unstable. He was less than a year old. Eventually he was euthanized. And I lost a friendship over it. Somewhere they had gotten very bad advice.
After owning many dogs, I will no longer own an unstable dog. I think people need to be careful about this. There is a big movement right now with dog rescue. Dogs come from some horrific circumstances, but also some circumstances where they may have been rewarded for bad behaviors in their previous lives, or a lot of other unknowns. Not only are they in peoples' homes, they're out among us. I don't like a lot of what I see, not only in how dogs are treated, but even how they're played with (rough, with bite encouragement). It's discouraging. Just as our world has changed in a lot of ways, so has dog ownership, as well. I'm not exactly sure how we got here. Dogs shouldn't be teased or encouraged to bite, EVER. Ideally you spend time with them to develop an actual relationship that is respectful (both ways) and fun. That takes time. A dog can be temperament tested and do well, but if it's not continued, problems can develop.
So yes, I agree with a pp that a dog on the sofa or bed is not the whole story. There are many ways that people show leadership with their dogs. The biggest one is just being there for ongoing interactions day to day where the owner directs the dog on how to act (and how not to act) until a mutually respectful bond develops and life is happy and predictable between you both (or all, if it's a family).
Good Owners, Great Dogs is a book that every dog owner should read.