There used to be a parade of stray and feral cats living in or around our house. One cat adopted us. Jenya and I named him Alexei. He was the worst cat ever - he refused to clean himself, he sprayed pee on everything, he scratched us, he would press his pointed paws into our backs as we slept. But we loved him and his bad attitude.
One morning, much too early, I woke to the sound of grinding out in the backyard. What the hell was that? I pulled the curtain aside and squinted into the daylight - it was a damn squirrel gnawing on a decorative cow skull we had hanging on the porch right outside the window.
I tried to scare it away by shouting at it. "Hey! Pssst! Get outta here!" The squirrel looked up at me for a second as if to say, "Really? Whatever, dude." And then went back to gnawing. Again I commanded it to leave but this time was completely ignored.
Meanwhile, Alexei was curled up at the foot of the bed, ignoring the commotion. Among his other faults he was also completely useless as an anti-rodent defense. Well, I knew this - but the squirrel didn't.
So I scooped Alexei up - he was all like, "what the fuck are you doing, bro?" and hung limp as I presented him out the window. "Hey, squirrel asshole - I got one of these."
The squirrel took one glimpse at the big orange cat dangling from my hand and fled the yard as soon as possible. Alexei paid no attention to the running critter. Instead he just writhed a bit, clearly wanting to be brought back inside because whatever was going on was total bullshit. I plopped him back on the bed, he groaned a bit, then we all went back to sleep.
In my experience, every cat's personality is distinct and unique.