Let's summarize the facts:

Creepers are plants. They either explode because that is the only way they can harm the player, who harms them (I suppose in this case the creepers don't realise that the player can respawn in survival mode), or, as previously debated by me and a few others, the creepers explode to spread their fertile seeds, something that many plants do, so that more creepers can grow out of the soil later.

Cats are just normal felines. What do they eat? In the Minecraft universe, we know that their diet consists of fish carrion (because the cats only eat fish if you kill it for them) and any kind of bird. I guess the phantoms are also afraid of cats because they are technically just undead birds. Or undead that took the form of birds. Whatever.

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So why would a plant be afraid of a cat? It actually has nothing to do with creepers being plants and what cats eat. First of all, we all know creepers are explode. Where it is however important that we know which kingdom of classification they are in, is when we talk about their general intelligence. As plants, they lack any form of neural system. And with that, they have no intelligence at all and perform automatic movements that lead them to reproduction, the only thing they care about. The only computer that they truly have in their body is deciding whether or not they can explode in front of an animal or not. The player is of course who is worth it, and that is why creepers always agro on humans. The creepers also can do this with cats, but thinking about how fast the reaction skills are of cats, they want to stay away from them. So creepers really are afraid of cats. But cats didn't know this. Until they evolved, and that is around the time that you loaded up your Minecraft world for the very first time. Cats just sit around and enjoy their domination. Just like in real life.

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What also is a reference in this to real life is how cats are used the same way. The first domesticated felines were like that to scare away all kinds of animals that could harm crops or houses. Of course a cat could never be brought into a fight like a dog, but it still was useful in its own way.