The reason the US government is arming Ukraine aligns with humanitarian reasons. There probably is some humanitarian motive but it is also within the best interests of the United States, NATO, and the EU that Russia be kneecapped for what they did.
The rules of the world since the late 1940s that most countries have adhered to and has been reinforced in a number of occasions is that the borders of every nation is fixed at their late 1940s locations or at their locations as set when a larger country broke up. Any country who violates the borders of a neighbor gets sanctioned at minimum and often much of the world will back military action against the aggressor.
The European countries are especially serious about this policy. They have deliberately surrendered old territorial disputes going back centuries in the name of keeping the peace on the continent. The Europeans, especially the western Europeans, have been hyper-reactive to any kind of armed conflict in Europe.
As for the earlier question about Russia losing. In a war, the aggressor needs to continue to take ground, or hold the ground they did take against insurgency. If they fail to do that, they are losing. The United States failed to stop the insurgency by the North Vietnamese and lost. The US failed to stop the insurgency in Iraq and Afghanistan and lost. The Germans lost momentum in their invasion of France in 1914 and lost. The Russians failed to stop the insurgency in Afghanistan and lost.
For a defender, all they need to do is hold on vs the aggressor.
It's very rare in the history of warfare for an aggressor to lose momentum and figure out how to get it back again. Once momentum is lost, the end is pretty much inevitable. There are different flavors of outcome, but generally the aggressor ends up leaving with their tail between the legs eventually.
