Part of it is the way snakes are kind of lumped together, since they generally look similar, a long tapered noodly thing. Big snakes are just bigger noodles and small snakes are small noodles. This is different from fish, which look pretty different from each other. People are generally scared of sharks, but probably not goldfish. Since it is harder to differentiate between dangerous and harmless snakes, it is easier and effectively safer to just assume all snakes are dangerous. The easiest way to 100% avoid dangerous snakes it to 100% avoid all of them.
Another problem is restraining snakes. Usually when people take their pets outside, they have a harness or leash. That way people who are uncomfortable with dogs or other animals know the owner can restrain their pets from attacking others.
Photographs are a great way to introduce people to snakes. I sent a few pictures to someone I knew who did not like snakes. Ball pythons are great for this since they are super cute. When she visited, she asked to see my ball python and gently touched him with one finger. She is still uncomfortable around snakes, but progress is progress.
I actually think snek memes have helped out a little with this issue. It somewhat ridicules some of the fears we have of snakes. When you see a snake is something that can be gently booped like a dog or cat and shies away instead of attacking you, it helps put things into perspective. Even when there is an angry snake, it says something like "heck off". Most snakes are not angry and aggressive because they gain a satisfaction from attacking and scaring humans, but are acting defensive. A snake definitely does not benefit food wise from killing a human, unless it is a gigantic snake, while cats and dogs have been known to eat dead humans.