My educated guess about Obama's core belief is that first and foremost he wants to go down in history as a successful first black president, and that in order to be considered a success, Obama tries hard not to rock the boat and does not challenge the establishment.
This is why he didn't close Gitmo, why he outsourced torture, why he supported indefinite detention in violation of Habeas Corpus, why he uses drone strikes, why he's still fighting Bush's wars, why he waited so long to come out for gay marriage, why he finally came out for gay marriage (the majority now supports this), why he bailed out the banks, why he propped up housing prices, and why he takes what he believes to be the centralist position -- although it's not because the right has more so far to the right.
Ultimately, Obama is a bad president because he's too worried about looking like a bad president. Thus he just goes along with what all the power interests already want. Obama doesn't attempt to change things other than that disastrous health care compromise in which he gave up all the important points. Obama doesn't threaten the power of the establishment.
I agree with fighting income inequality and I wish him well if that is his true intention. I think innovators and job creators should become fabulously wealthy, but I also think that most of the wealth doesn't go to these people and instead goes into the pockets of assholes who sit on the couch speculating and eating up dividends and parking full oil tankers off the coast to drive up the cost of gasoline.
If the capital gains rate returned to 28%, Buffett and Gates would still be worth billions of dollars, but at least the federal budget would be a bit more balanced and a few more dollars would flow to people who work for a living.