U aren't "socializing" him, nor are U letting HIM socialize. // U're letting a rude dog, with no social-skills, off-leash in an environment where he inevitably causes tension & bad feelings - with the other dogs, & the other owners. socializing a puppy
has a very specific meaning -
it's the deliberate exposure of that pup under CONTROLLED circumstances
to other living beings, with whom U want that dog to get along in some way, for their lifetime.
U might want the pup to tolerate them, ignore them, or befriend them; U might want the pup to relax & accept handling from them [the vet, the groomer, dog walker, vet-tech...].
U might want the pup to treat them as family members [the household cat; the house-rabbit; the pet parrot]. / Even more specifically, every socializing experience is supposed to be a HAPPY one for the pup, creating many pleasant memories.
Ur dog is 2-YO; he's no pup, & he's well-past the socializing window - anything past 6-MO is considered B-Mod.
Taking the leash off & standing by to watch him be incredibly rude isn't "sociable" at all, in any sense of friendly interaction.
U need a local trainer to help U; someone with both experience & credentials, who uses humane, science-based, rewarding techniques - not someone who's riding The Dog Whisperer's coat-tails.
If they so much as mention 'packs' other than as a cute term for the family, i'd RUN not walk in the other direction. If U give us some nearby city or town, someone on the Forum may be able to refer to a specific trainer nearby.
Plus, U will need some extremely-tolerant dogs
to work WITH Ur dog, & teach him some manners.
Humans intervening to get him away from a dog he's molesting, or interrupting in an attempt to "teach him" by removing him from the chance to play, doesn't work anywhere near as well as direct, pointed, immediate feedback FROM ANOTHER DOG.
That dog will have to be extremely forgiving, patient, & sociable - b/c if they're not, his behavior will spark another tiff, & deservedly so; he's an ignorant jerk, which isn't his fault, but it's completely unacceptable to inflict him on other dogs in any other context than as behavior modification
for his own outrageous behavior.
Where do U live? - U-S, or elsewhere? // there are many good, reputable trainers, & we can surely dig up a few referrals, for kind handling & effective training.