The Diaoyu Islands were probably under Chinese control (if that term can be applied to a bunch of uninhabited rocks — like the rocks that probably litter the shores of most countries and are “under their control”) until 1895, when the Japanese annexed them under a treaty signed after the first Sino-Japanese war. The US took control of the islands after WWII, and, for obvious geopolitical reasons, gave them to the Japanese in the 70s. China and Taiwan immediately protested. This is an old issue (and the fact that Taiwan protested too says something about how this issue resonates among the Chinese citizenry). This issue is of concern to the citizens of China, as much as the Kurils are of concern to the citizens of Japan and Guantanamo Bay is to the citizens of Cuba.
As with all these issues, the media plays it up for news (think 19th century yellow pages) and the government plays them up to win support (think spanish-american war, Bill Clinton’s lackluster response to the world trade center bombing in ’94, etc.). This process is not “evil”, “manipulative”, or “a product of state-controlled media” — this is politics.
As far as China is played up to be the aggressor, the Japanese are the ones who made war on China, annexed the islands, and received them back to the US. You can say we are trying to redraw the map, or the Japanese redrew the map and are trying to deny it. Incidentally, to gain popular support, Shinto Abe’s government bought back the islands from their private owner, reigniting an issue that had simmered nicely for decades.
The islands are not all that valuable — billions in oil reserves are not worth billions in aircraft carriers, destroyers, and hundreds of aircraft destroyed.
The US needs to exert power and influence (and get popular support, citizenry screaming for response, blah blah blah blah — same as the Communist Party).
Plus, the US totally is trying to contain China and limit its power(average great power politics)— and if China backs off the Diaoyus, China “loses” this round and loses power and prestige.
THIS IS GREAT POWER POLITICS.