Half....Really?

I found this mildly disturbing today:

Nearly half of US households escape fed income tax

Now don't get me wrong I don't like paying taxes, but I do understand their importance, they provide for our police and fire protection, schools, roads, agencies that keep us safe, healthy, infrastructure, power, water.... I mean the list just goes on and on. BUT what if the people are profiting from taxes? Heres the example for an average 4 person household

"The family was entitled to a standard deduction of $11,400 and four personal exemptions of $3,650 apiece, leaving a taxable income of $24,000. The federal income tax on $24,000 is $2,769.

With two children younger than 17, the family qualified for two $1,000 child tax credits. Its Making Work Pay credit was $800 because the parents were married filing jointly.

The $2,800 in credits exceeds the $2,769 in taxes, so the family makes a $31 profit from the federal income tax."

Seems like if we all have healthcare (sorry insurance) we should all pay some taxes right? Something just doesn't seem right. So now we're sticking half the population with not only all the tax responsibility but they also pay other families that don't pay at all. I'm bothered by this.