I don't know what others believe or think, but I know what I used to think:
You can't "make" a drive in a dog. Food doesn't work if your dog doesn't care about food.
When you don't have food, they won't listen.
Rewarding everything, all the time will just make them value praise less.
If a dog is smart enough to do X, he should be smart enough to learn Y without making it a big ordeal.
Dogs need a leader, or they will lead you.
Not correcting bad behavior makes the behavior worse. You can't correct bad behavior by ignoring it.
So on so forth. I was one of "those" people. The only dog training I ever heard of was on TV, by CM. I was pure PR on some things, like potty training, but everything else sort of escaped me. I hated VS on Animal Planet, because I thought she was just shoving food at dogs for no real reason. There wasn't any behavior to reward, so I thought it was pretty stupid.
what arguments do you have to counteract them?
If you were minding your own business, maybe talking to someone and window shopping, and your friend all of a sudden came out of no where and started beating and yelling at you, would you know what you had done wrong? How would you immediately correct your behavior? Would you ever trust that person ever again? Would you fight back?
I've made a lot of people think by just putting it in easy terms for them, even if that's not how I personally figured it out. I use similar scenarios for dog food, too. Like the Mac and Cheese and Hotdogs. Yeah, you feed your kids that every day, they'll love you for it, and they'll survive, might even get fat. But is it really healthy for them? Ditto with corn. Do you ever see dogs going hayday in a corn field? No. Now give them a steak, and see what reaction you'll get.
When you put it SO simply and put the person in the dog's shoes(or paws), I think they get it a lot easier than with science and mumbo jumbo they've never even heard before. Step down to common sense level, and build from there.