I had seen mods that allow you to pet your dogs, but can't find any that allow you to pet your cats, which is a shame, so I made it with MCreator.

To pet your cat, you just need to shift + right-click it.

By petting your cat, you have a 2.5% chance to get a string (Because cats have fur), and petting it for the first time will also give you an advancement.

But also be aware that the cat has a 5% chance to bite you and walk away when you pet it.

This mod also works fine with carry on which I recommend you to get it as well, so you can both pet and hug your lovely Minecraft cat, but with that mod, you will need to place an item in your offhand to pet your cat. May not work now

You can craft a cat comb to replace your hands if you are using the carry on mod. However, using it would increase the chance of dropping string and the chance of the cat attacking you with more damage.

To find the data pack version (No mod loader needed!): https://www.curseforge.com/minecraft/data-packs/pet-your-cat-datapack-edition

My other mods highlight

Logical Crafting: https://curseforge.com/minecraft/mc-mods/logical-crafting
Mutated Food: https://curseforge.com/minecraft/mc-mods/mutated-food

Pet your cat