For a long time, I thought that dogs were spayed and cats were neutered. The cat I had when I was little was always getting into fights and spraying in the house, which naturally annoyed my parents. So, they had him neutered, which they explained would cut down on this behavior, and make the spray less stinky. So, I thought neutered meant neutralized. Like, there was something was added to the cat that neutralized the smell of the spray, and made him neutral in fights. After all, my parents had explained that saying "Switzerland is neutral" meant they didn't get in fights with other countries. I'd heard the term "spayed" and knew that it was similar - since I knew that cats got neutered, I assumed that meant that dogs got spayed. After all, the phrase is "spay or neuter your pets" and there's two kinds of pets, dogs and cats. Having different words for different animals made more sense to me than different words for the genders of both.
Now that I think about it, "neuter" does have a lot in common with "neutral", duh, same root. The animal becomes of neutral gender. And it does result in an animal that is less aggressive.
A childhood belief about cats and dogs

others believed things like this
- My sister and I thought cats and dogs were the same animal, the dogs were male and the cats were female.— Paul
- I used to believe all dogs were male and all cats were female. I still call dogs "boy" and cats "girl." — Kelly F.
- I use to believe that cats and dogs were the same species; cats were girls and dogs were boys.— poopcrystals
- We had a male cat that wasn't neutered. I thought his testicles were just the cat version of a butt.— Robyn
- When I was little, I used to think that cats and dogs thought in English???— Isabella
- I thought that all cats were the females, and that the dogs were the males.— opps guess not