People often assume riders are 'arrogant' because they are quite literally looking down on people standing on the ground. And why is this person a 'twerp'? I suppose you might be trying to be funny, but asking someone to do a trivial thing like getting off their bike for a moment is nothing when compared with the fear and risk associated with being on board a bolting horse.
They are a twerp, which i accept is insulting, because they have taken a horse which apparently cannot cope with cyclists in close proximity onto a path where that specific event is almost certain to occur. They compound that by refusing to clear up the muck deposited in the middle of the narrow track.
As for all the "scared horse" stuff maybe you should remember some of us didn't grow up around horses and have never ridden them. To me a few hundred kilos of muscle equipped with steel shoes and a rider worried about controlling it is pretty bloody terrifying.
By the way i do get off in these circumstances, purely out of self preservation. And i usually end up clearing away the mess. I simply don't understand why horese owners don't have the same obligations as dog owners.