So, ever wondered why people have pets? It varies. Different pets attract different people for different reasons. If you want attention, get a dog. If you want something to spend money on, get a horse. But cats... why do people get cats?
If you think about it, cats don't make much sense. They do their own thing, you have to clean the litter tray and feed them every day, other than that they occasionally demand attention and petting, and they occasionally (often if it's cold) sleep in your lap while you're doing sedentary stuff. Why is this good? If you're a modern ape and have a gas heater and some blankets, what do cats really bring? Other than being really smug when they're happy. Really, really smug, and satisfied and happy.
See, humans are pack animals who historically (in the anthropological sense) have relied a whole heap on our social group for our survival. As such, we're empathic creatures. We've evolved to distill some happiness from the comfort of those around us. And it just so happens that cats with their little fuzzy faces and their little fuzzy paws are perfectly featured to express comfort, and relaxation, and happiness, in body language that we humans can instinctively read.
This is why we keep cats as pets. They provide companionship, and they are often much more concerned about our wellbeing than we give them credit for. But when it comes down to it, we keep cats to be our happiness proxies. All of the things we wish that we could feel, they feel. (Or at least they look like they feel... who knows what another creature really feels?) But if you've ever given your pet cat a scratch on the jaw, seen her stretch luxuriously and then settle back in to sleep, and headed on your way to work feeling that bit happier for thinking "at least she gets to sleep in"... then your cat is your joy surrogate. She exists in your life to be happy. You do whatever you can to keep her that way, because just by being happy, she makes you happy, through this mechanism of empathy.
Even if you have to get up and go to work when you really don't want to, your cat doesn't, and your cat's happiness can be enough for the both of you.