You're not being sufficiently specific as to "which wealthy" or "which poor" should be "equalized" - nor what any such equalization should actually mean.
Clearly, many "poor" are poor because of their (poor) choices. Others are poor because they can't (currently) overcome their adverse circumstances. Others still are poor because they're being actively cheated by the powers that be. This is the one "poor group" which is steadily growing in size.
On the other hand, many "rich" are wealthy because of how hard and/or how smartly they work. Other "rich" people are wealthy because they inherited or otherwise "stumbled" upon their wealth. Others still - the majority of the current rich - are wealthy because of legalized cheating and machinations.
Where are the "problem" areas here?
* On the "rich" side, clearly, it's the last group: those who cheat to achieve their wealth.
* On the "poor" side, the REAL problem are those who are constantly being cheated out of their potential.
* All the other groups can be left out of the equation.
So now the question can be rephrased: why do people allow themselves to be impoverished by the ultra-rich cheaters?
And all of a sudden, things start coming into focus. You can now ask yourself two followup questions:
* "who are those cheated poor?" - as well as
* "who are those unfairly rich?"
If you do any sort of impartial analysis, resisting the temptation to apportion blame along party, ideological or economic lines - you will NO DOUBT conclude that the blame rests squarely in TWO areas:
1) The cheaters: The corrupt government (most especially the power elites within the military and security services) which colludes with certain corporations (cronies who are given no-bid nepotistic contracts) as well as with special interest groups, lobbies and... many corrupt unions.
2) The cheated: The useful idiots among the people and their representatives who have NO IDEA that they're being screwed, and yet they applaud virtually all legislation which is being introduced daily with the specific purpose of disempowering... themselves.
By allowing themselves to fall for "capitalism bashing" (without realizing that the situation has NOTHING to do with capitalism, but EVERYTHING to do with socialist totalitarianism), they direct their powerless anger at the WRONG ENEMY. And thus, there is NO CHANCE of EVER "equalizing" incomes - or more appropriately: achieving a FAIR income balance.
Want fairness? Hold the government to account.