Note that when I say "slowly conquering", I'm referring to something less than conquering (initially).
By controlling all shipping in the area, this would give them great power over the affected countries.
Whatever language is best, they want pretty much the same thing as America, the ability to project power in a strategically important area of sea. Both are using the various options they have on the table for doing so.
There is no reason to see this as a precursor to an attempt to conquer any of their neighbours. China's economy is export driven and couldn't survive it in good shape (possibly leading to civil unrest), the resource cost and instability that result from such actions would not be desirable, and expansionism isn't part of the national psyche in the same way it is in other parts of the world.
I don't see that Americastan is aiming for such control.
It appears that our goal is peaceful autonomy for those in the area.
That may well be a part of it, but it's not the whole picture.
Part is the typical penis measuring contest that goes along with power politics.
Part because Asia is of increasing importance globally, which is part of the reason for Obama's 'pivot' towards Asia. Unsurprisingly, China also wants a say in what happens in the neighbourhood.
Part contingency in case of future problems. Again, not surprising China wants to do likewise.
Both sides are protecting their national interests. China's national interests don't extend into conquering any of its neighbours though.
One should not criticize one's many many objects of derision too often or when it's not germane.
Well their actions didn't work out too well in Ukraine, and they are creating tensions in Asia now. The further they push China and Russia, the more they will push back. Their policies have been unnecessarily antagonistic, by insisting they have the right to project their power right onto the doorsteps of these countries.
Just as a hypothetical, would America be fine with China and Russia constructing military bases in Cuba, Mexico and Canada, putting troops right on US borders and asserting their right to patrol shipping in the North Pacific and North Atlantic oceans?
This isn't to say they should leave the entire region to China, just that a less antagonistic approach would be better. Just as it would have been to stop the NATO expansion at the edges of what has traditionally been Europe, rather than trying to get the likes of Georgia and Ukraine into the fold which were historical Russia, rather than Europe.