Because people are different. Some people will spend more than they make, while others will spend less. Eventually it will end the same as it is now.
It is funny this is mentioned, because here in Costa Rica, there was a living example of this.
Back in the middle/early part of the 20th century, there was a lot of unused land in a place called Guanacaste. To help develop it, the gov gave out equal portions of land to different families so they could work the land/raise cattle and help develop the economy of that area.
A few decades latter and guess what happened? Slowly but surely, the estates consolidated. Some people worked hard, others drank hard. The ones that worked hard slowly bought up everything from the vast majority that didn't.
Now that is not to say that inequality isn't a problem. It is. Wealth consolidation eventually leads to rigid class systems that stifle innovation and development. A huge reason the USA managed to surge as a nation was because it offered a fluid class system and it was competing with countries with rigid class systems (of course there were other reasons; vast-untapped natural resources, a large amount of arable land aquired for pennies on the dollar via bloodshed, a culture of hard work, good climate, wars/political issues in Europe, etc)
Now, just because I mentioned inequality as being a problem doesn't mean I know a solution to it. I don't.