A lot of the problems that the US faces in the world is due to our idealism. We hold ideals that are very attrictive, but have often failed to live up to them. If we want the US to be better liked we need to either start following those ideals, even when doing so costs us in the short term, or become less idealistic so that the additional leaving of hate that comes from acting hypocritically doesn't happen. Far too often in the Cold War and now in the War on Terrorism we have tolerated and even supported "good" dictators. For instance when he attacked Iran Saddam was a "good" dictator, while when he attacked Kuwait he was a "bad" dictator. His actions were the same, but we objected only when we didn't like his choice of target. Whether consistent idealism, consistent realpolitik, or our current mix is the best foreign policy for the US depends upon what you want from it. If the goal is to be liked, it is the worst policy, but being liked is hardly the most important thing for the US to worry about.
You hit the nail on the head there. The reason the US is disliked is because we don't have a consistent foreign policy. Sometimes we support dictators and terrorists (sorry, when we like them, they are called "freedom fighters"), sometimes we oppose them. It has nothing to do with this "they're jealous" BS. They hear us talk about spreading freedom and democracy and then wonder why we support some tyrrannical regimes.
We should just come out and admit it; we don't want everyone to have a democracy, we want everyone to have a government that is friendly to the USA. Whether that's a democracy or a dictator, we couldn't care less. That's the USA's foreign policy; it's based on what's best for big business in this country, not what's best for the people of the country in question.