The core spirit of the Monroe Doctrine was: "this is my house, betches!!!"
It was already abundantly clear by that point that the US would be dominant power inthe New World. So excluding the influence of the European Continental powers meant American hegemony, a status while is preserved even to this day.
From China's perspective, the US plays the role of the Continental European powers, distant nations sticking their noses into affairs far outside their natural geographic reach. And what China wants, that is to push American influence out of the western Pacific, comes from the same "this is my house betches!!!" school of thought.
China sees itself as the natural hegemon of the region and has built its long-term strategy to realize this goal. To do that, it has to kick out the influence of the US just as the Americans had to kick out the influence of the Continental European powers from the New World.