I'm curious how you know what Obama "knows"
Everybody knows the tax system is extremely unlikely to change - and everybody acts like that's a big secret. We might cut taxes a bit here while raising them a bit there. We might raise a tax rate here and add a loophole there. And so on...
He frequently included himself when talking about millionaires and billionaires
Did he make a million dollars last year? Did he ever say that HE or anyone should voluntarily over pay
I've no idea if he made a million dollars or not - it's irrelevant. If he really believes he's undertaxed (he said he is) and is rich (he said he is) and he believes that the rich ought to pay their fair share (he has) then he should prove it by voluntarily overpaying.
The argument "Well, I feel like I ought to pay more and make the argument that it's my moral duty to pay more, but I'm not required to under the current tax code so I won't" doesn't hold water. Either you believe what you say and stand by your convinctions, or you either don't believe what you say or don't stand by your convictions.
There are certainly issues where one could legitimately call Obama a hypocrite but I don't see it on this one.
It's hypocritical to argue that you don't pay enough in taxes and to not lead by example by choosing to pay enough
today even if the law doesn't mandate it.