Spirit, please understand no one is telling you you are a bad horse owner - on pretty much other thread on this forum everyone would agree with you. But you entered a thread where the OP uses Positive Reinforcement training, so we gave her suggestions based on the style of training we use.
Now I think you're getting offended because we're using scientific terms to define things, but I think you're putting an emotional connection to the terms.
First of all you (and most modern horse trainers) rely mostly on what's called (scientifically) "negative reinforcement"
To understand the difference between positive and negative reinforcement, as well as positive and negative punishment - first you need to get rid of the emotional connection with all of those words. Positive simply means "adds" Negative simply mean "subtracts" Reinforcement= "causes and increase in that behavior" Punishment="causes a decrease in that behavior"
I hope this image can explain it better than I can:
Now you're right giving your horse a pat could
be positive reinforcement. In our training style, we typically use a food reward because it's what's called a "primary reinforcer" meaning every animal is born desiring food, it takes nothing on our part to make food valuable, it just always is - horses are perfect for this because they eat 24/7 (versus predators which may eat a few large meals infrequently). A pat or a praise word is what's called a "secondary reinforcer" it's something that has no meaning, or may even been aversive to the horse (many horses are not a fan of patting - my TB stud for example cringes as gentle strokes, very thin skinned). But when the pat or praise is frequently connected with a release of pressure or with a food reward eventually it becomes reinforcing for the horse - but that takes time. For example the sound of my click becomes a secondary reinforcer, I never stop backing it up with a treat though.
As for your horse respecting you - if he respects you and you don't use treats that's perfectly fine. You are free to train your horse how you like and I think most horse people would agree with you about the "no treats" thing. But we are different. I use treats to train my horse - it allows me to train them using minimal to no pressure and allows me to never need punishment.
As far as horses respecting you or mugging you for treats - I have 17 horses (total) that I train, 3 of my own are included - the rest are rescues from every walk of life, from damaged show horses to completely feral horses never handled before. I use Clicker Training (positive reinforcement training) on all of them. I can promise you none of them will bite me, invade my space or be otherwise rude, regardless of whether I have food in my hand or not.
If you have something that works or you - please don't less us burden you with more information. But if you're interested in learning more let me know.
Here are some other references you might want to look at to understand more the difference between positive and negative reinforcement. The Dominance Model and Horsemanship by Equine Ethology Are Dead | enlightened horsemanship through touch aboutclickertraining
This is a great thread on here, the first couple pages have detailed descriptions on the science behind Positive Reinforcement training: Clicker Training: Challenge Accepted