It’s pretty obvious why China would want its own carriers - to secure oil, for one thing. China is increasingly dependent on foreign energy - energy which is getting in ever-shorter supply. You can imagine a world in the medium-distance future (say, 20-50 years out) in which there is real contention for oil and other resources, and the countries that can project force can impose blockades (or break them), promise security to nations in exchange for mineral rights, etc.
For example, there is going to be increasing tension over northern waters above Canada. As the ice melts, it exposes new areas for deep-water drilling, creates shipping lanes, and in general becomes a new source of untapped wealth. Russia and Canada are already staking claim over it - Canada is building new military vessels to defend those claims, and so is Russia.
Plus, a carrier group is kind of an ante you have to play if you want to be considered a superpower. China has ambitions to be a superpower. Superpowers build alliances around the world, and then are expected to defend them. That requires power projection. It’s why the U.S. has ten carrier battle groups.
All that said, I think China will find it a lot harder to float a viable CBG that it imagines. As others have pointed out, carriers go to sea with a whole flotilla of support ships including cruisers and destroyers. That in turn creates big logistical problems (you’re moving a LOT of fuel across oceans constantly). The logistic tail has to be protected as well. So then you need subs. And since the Americans have hunter-killer subs, you need your own defenses against those. And so it goes. Carriers are just one part of an extremely expensive, high tech infrastructure. The U.S. has been building on and perfecting its carrier strategy for seventy years. It has a huge head start over anyone else who would try.
In addition, what makes the U.S. so effective is its overwhelming advantage in organization and communication. AWACS, satellites, computing power, and advanced military networks that are hardened and tie it all together. Hell, America has the ability to launch drone bombers or surveillance craft from American soil, fly them over conflicts almost anywhere in the world, and fly them home without landing anywhere else.
China currently has so many holes in its military technology that it couldn’t hope to field a battle group of any kind of effectiveness for a long, long time. But then China tends to think in the long term.
Then there’s the cost. A carrier can cost $5 billion or more to build. An entire carrier battle group could cost $20 billion including support, aircraft, etc. And a CBG can cost several billion dollars per year to operate. China’s GDP is still only about a third of the U.S.'s, so a carrier would cost China three times as much in terms of percentage of GDP. Carrier Battle Groups are barely affordable for the U.S., so it’s hard to see China being able to afford to do it right.
Because carriers take a LONG time to build, test, float, and equip, countries who want them have to plan for the world that may exist 30 years from now, not the world that exists today. So it’s no surprise that China might be thinking about carriers. And maybe they can get away with more limited support on the theory that the U.S. isn’t about to attack Chinese carriers, and no one else has the capability. If you just want to project power to defend, say Venezuela in exchange for oil rights, and you’re really just playing a big game of chicken, maybe you can cut some corners and get away with it. For that purpose your defenses don’t have to be impregnable, they just have to be reasonably credible.