... is only making half of the "average American" by the measure most people probably think of (add up how much we all make and divide by number of people, i.e. mean income).
That's just bad statistics. When you speak of the "average" member of a population, as in the phrase "average American", the measure you want is always the median, not the mean. You can talk about "mean income" all you want but that has nothing to do with the "average American".
What SHOULD be surprising is that most Americans are making less than half of the [mean income].
I don't find it surprising at all, actually. The development of stable wealth is a process that requires saving and investing over the course of multiple generations, which runs counter to the current popular mania for expecting individuals to pull themselves up by their own bootstraps. At it stands, those who come from families which did not suffer from this particular mania tend to be vilified as "the 1%". If the 99% truly desire equality they ought to be learning a thing or two from the 1%, not trying to destroy what the 1% have accomplished through discipline and foresight. There is nothing "unfair" or immoral about wanting to give your own children a better start in life than you had for yourself. If more people thought that way the distribution would not be so uneven.
But if you want to hoard all the money, be prepared to pay for everything, because nobody else can.
It's not about the money. The wealthy don't tend to hold all that much money, as a matter of fact—they hold investments. What this is really about is the capacity for production, a.k.a. capital, and the mindset which creates and nurtures it. More than that, it is about those who spent their savings on short-term consumption envying the rewards earned by those who invested in the capital which enabled their consumption, and vilifying and punishing the investors for having the audacity to produce the goods they demanded at prices they were willing to pay. In the end, seizing the investors' capital will not change the consumers into investors. The capital will simply fall into disrepair, consumed by an ungrateful public for a short-lived gain.