I do think there's something that happens between dogs themselves that most of us don't quite fully recognize or understand. And I don't fully understand it, either. But I have been able to observe it and try to make sense of it for my own understanding. One thing I do know is that things becomes quite complicated when dogs are in pairs or packs, when they're leashed and not leashed, when they're in a controlled situation (leashed and unleashed) vs an uncontrolled situation (leashed and unleashed), etc.
Prior to my current dog, I had two German Shepherds who loved other dogs and would be quite happy running around playing in a dog park. They seemed to project to other dogs that they were open to play and "friendships" and were relatively submissive, apparently. Anyone could bring their dog(s) in my yard and all would play. OTOH, my current dog loves people, especially kids, but doesn't particularly care for other dogs even though she will tolerate them and even walk with them without an issue if they leave her alone. But somehow, many dogs pick up on "something" with her and want to challenge her. I believe it is probably about dominance. It has been very interesting to observe, ie the differences between walking her and walking my other two (and all of them had virtually the same training and same socialization by me from puppyhood and in extensive group class with a professional trainer to fully off leash and hand signal trained). The difference, as best I can tell, is themselves, their personalities and the persona they project. My current dog is a dominant female and projects that to others, a few of whom want to challenge her, most of those being males. (Laugh O Grams, this could possibly apply in your case as well.) Dogs, in their interactions even from far away, sense something we can't see or "get".
Bottom line, in a dog park, it's a free for all. There's all this "stuff" happening among and between the dogs (and people) with little control or even wherewithall by owners or power to do much about it if a problem occurs. People seem to think that all dogs love other dogs and love to play with eachother, that only untrained or unsocialzed dogs cause problems (which is generally true but discounts many other factors that come into play), that big dogs cause most of the problems, that little dogs can do no wrong, that bully type dogs are all bad, blah, blah, blah; and to not recognize things actually happening like dominance issues, simple dislike of another dog type or personality (some dogs don't like sporting breeds, for instance, or hyper dogs, and it is never a good idea for one dog to be in another dog's "face" - this is etiquette that needs to be taught and enforced as it is a cause of many dog fights), dogs' breeds and/or roots in behavior and habits, etc. Cause in reality there's all this other stuff going on and it can led to problems if left unchecked. (Does anyone remember the Dis poster a few years back whose Weimeraner was killed by other dogs at a doggie day care in an uncontrolled situation?

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I am a big fan of group training for dogs. Dogs are together, yet under control, with a trainer right there to point out problems to owners and to convey how to institute corrections right then and there. It's great, because everyone stays safe and people learn what mistakes they're making with their dog, and how to control the dog, etc. None of which occurs in a dog park. All you get are people yelling at eachother if their dogs aren't getting along, but what they fail to see is how their own dogs are either consciously, unconsciously, inadvertently or etiquette wise contributing to the problem, or things they could have done to prevent problems, etc. Prior to owning a dominant dog and knowing what I know today about dogs, I might have mistakenly thought a differenty way, too. But I know more now, having learned along the way with my own dogs and taken on dog training and behavior as a hobby over two decades ago. (Now you can see where my mind is.

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Which is why, with my current dog, I'll avoid dog parks. Being a GS she will almost always get the "blame" even if it wasn't her that caused the problem in the first place (at least not intentionally; there's not a lot I can do if she projects dominance to other dogs in dog speak, lol). I'd rather do our own thing under conditions I can control and prevent problems as best I can and stick with dogs we know get along well together.