Their Navy is way behind that of the US, they aren't going to catch up any time soon, if ever.
Correct on the first count, completely wrong on the second. Within the next 15-20 years China are going to become the dominant naval force on the planet, this is something warhawks in Washington and Moscow are aware of and in the case of the former they are attempting to do as much as they can to mitigate/prolong it as much as possible (in the case of the latter they know there is nothing they can do about it). The reason for this, is like always, HMS Dreadnought.
To explain (mainly for those with limited knowledge of/interest in naval combat, but it's probably interesting nonetheless), HMS Dreadnought was a battleship launched by the Royal Navy in 1906, it was the most powerful most advanced battleship ever constructed and it spelled the death of the British Empire. You see, for the majority of the 19th century the British Navy had been practically unchallenged as the worlds most dominant naval power, and for good reason. The RN wasn't just bigger and more power than the number two navy, it was bigger and more powerful than the number two and number three navies combined! And this wasn't an accident, UK law dictated that naval spending must ensure so. So how did it go wrong? And what relevance is this to the rise of China? Simply put, HMS Dreadnought was so ground-breaking that it made all previous battleships obsolete, battleships are generally categorised as pre-Dreadnought battleships or dreadnoughts and nobody had more pre-dreadnought battleships than the RN. This resetting of the board caused all navies to essentially start from scratch and this allowed countries with comparable (or even superior) economies to Britain's to close the gap on the RN.
Then came WW2, and the rise of the US navy. I'm sure most of us have heard how at the height of the battle of Britain the Luftwaffe were shooting down our aircraft faster than we could build them. But another less known (on this side of the pond) feat is that at the height to the war in the pacific the US shipyards were churning out vessels faster than the Japanese could build the planes/ordinance required to sink them. Then towards the end of the war there was a Dreadnought moment once again as aircraft carriers replaced battleships as the alpha weapon. After WW2 the US Navy was number one and over the next few years the Soviet navy followed it into second place, the Royal Navy would never again reach it's pre-dreadnought heights.
And this is where China's ace comes into play, over the next decade or two the aircraft carrier is going to be rendered obsolete by the drone carrier, once again resetting the board, and China as the planets most industrious nation is going to be able to construct and launch drone carriers faster than any other nation on Earth. That's why the warhawks in Washington are calling for major spending increases to try and prolong the inevitable.