Do you keep your dog on leash at the beach?

Ok, so this is the first time as an adult I’ve had a dog. He’s a 1.5 y/o pit bull staffy mix. He’s SUPER friendly. And far from dog aggressive but he plays so rough, and does try to mount (we’re working on that). So I keep him on leash till he can calm down. Well yesterday was our first beach trip. He’s used to dog parks which are fenced in but the beach was completely open.

Every dog there was off leash. I’m so not used to that. So naturally I was nervous, mostly because I don’t trust the owners of the dogs and how they would react had my dog started to play. Anyway, there were a few times people had some out of control dogs that approached mine. The interactions went smooth because again. My dogs not aggressive. But this super bratty Frenchie that was off leash came and started biting at my dogs feet while we were in the water. I pushed the dog away but the owner got a bit upset with me. (Not gonna lie I pushed that dog pretty hard mainly to keep my dog from destroying him, I could see my dog wasn’t comfortable)

Anyway, there was a bit of an argument between us, I told her if her dog is a bad listener maybe she should just long line him but keep him on a leash. Especially since it says that the dogs need to be leashed at that beach. Of course since I have a pit my guys always the bad guy. (My dog ended up snapping at the frenchie, no contact or anything but it was enough to help get the frenchie away) luckily a couple saw what happened and took up for me. ( tbh that frenchie had been “attacking” other dogs all day)

The argument was about keeping your animal leashed. But she felt that because it’s a dog beach she’s free to unleash her bratty ass dog. The other dogs off leash didn’t attack and rarely approached other animals but for some reason her frenchie was not having it. I ended up just leaving the beach but it really frustrates me that people still keep their dogs off leash when they’re misbehaving.

I’m not a pro dog trainer, nor do I have a lot of experience with stubborn dogs. But my leash is my life saver especially when training my dog how to act off leash. So it blows my mind to see how careless others can be. Was I wrong for asking her to keep her dog on leash and pushing her dog?