Why does china not have aircraft carriers?

This is not true. China does have aircraft carriers. The People's Liberation Army Navy (PLAN) currently operates two aircraft carriers, the Liaoning and the Shandong, and is building a third, the Fujian. The Liaoning is a refurbished Soviet-built Kuznetsov-class aircraft carrier, while the Shandong is a domestically-built Type 002 aircraft carrier. The Fujian is a new-generation aircraft carrier that is currently undergoing sea trials.