I don't think anyone disputes that Russia is trying to be a power player in the region, and in the longer term, regain some of its old status in the world. It's doing that, not because it or its leaders hate us, it's doing that because it's good for Russia. What else are they supposed to do?
What I'm saying is that all nations do, or at least should, do what's in their interests. Now, wise leaders know that longer-term goals tend to be more collective, whereas short-term goals tend to be filled with conflict. The reason everyone seems to hate us in particular is because we are the most powerful nation around. If others want more influence, most of the time it comes from diminishing ours. That's why it often seems as if much of the world is always busy denouncing the US.
All the things Fog is listing are true to some extent, but their motivation isn't anti-American, other than as a means to an end. They're just being pro-Russian. The only way to defeat an enemy is to know him and his objectives. If the US makes decisions on the basis of the belief that "Putin hates the US," we'll be making the wrong responses, e.g. hate is something that can't be dealt with by negotiation.
If we understand the actual motivations behind their decisions, whether they are based on economics, military, or political power in a given situation, we can make the right responses in order to achieve our national goals.