Re: “if you don’t think there’s such thing as a ‘dirty stopper’ you’ve never ridden/owned xyz kind of horse/pony”…there are indeed some equines out there, often mares in my experience, that may full well know what you’re asking but are going to make sure you really mean it before they acquiesce.
BUT…as so many others have said, that does NOT mean the horse has ill intentions towards the person sitting on them: this is the human’s ego talking. It’s a rare horse that wants to hurt you…the vast, vast majority of what we call “avoidances” - sudden bailouts prior to a jump being such an avoidance - are simply the horse looking out for number one, because that is the one law of nature he must follow: he must survive. Sounds dramatic to you or I, but to the horse this is deadly serious business. It’s the reason why it takes so long to build a horse’s confidence but can take only a couple mistakes to completely destroy it.
So, in the case of the couple of “difficult” horses mentioned as justification for the term “dirty stopper” - there is nothing in the horse’s psychology that would even allow him to contemplate of doing things “just because”. There is always a reason, and that reason is always justifiable in the horse’s mind. If one hopes to change these types of horses’ thinking, one needs a level of perception, patience and skill that is far beyond what most riders can offer. Ergo, these types of horses need professional riders of the highest degree. Most of them never get that and so they get labeled as naughty.
Words matter, and the context in which they are applied matters. There is nothing accurate about the word “dirty” in this context, and it’s misleading to those who might not understand what reference is being made. If it takes an experienced horseman to understand the true context - as one poster suggested - that’s an indicator that the term is not truly useful or accurate and should probably be scrapped for something more appropriate. No one can possibly defend the idea that a rank beginner (or even a fairly decent but perhaps unaware rider) is going to hear the term “dirty stopper” and think anything other than “the horse is doing it on purpose to be bad”.