Argentina most likely leaked it to pressure the Americans into allowing their wanted T50 sales. Although this also benefits China, so it may even have been a mutually agreed ‘leak’.
The British have been increasingly caving in to American pressure to take sides against China. This could be an unsubtle reminder that doing so would not be cost free for the UK.
If China wanted to, it can offer JF17s on credit to Argentina, or even work out some sort of barter, like quota’d access to Argentine waters for fishing. It may be worth it for China to spend a few billions to fuck with the UK if it lurches too far in favour of the Americans, as a sizeable fleet of JF17 BLK3s with a large inventory of China’s latest and greatest AShMs would fatally undermine the RN’s ability to defend the Falklands. The threat of that would be a powerful bargaining chip to ensure the British stay on-side of the Sino-American Cold War.