We got a distribution from our 401k we already paid the 10% so why do we have to pay it again in taxes?

You don't.  The tax withholding in box 4 on the 1099-R is applied to taxes paid on the 1040 form line 25.   401(k) distributions are taxed as ordinary income.  The default mandatory withholding on a 401(k) is 20% so I do not understand why only 10% was withheld.

However, if you are under the age of 59 1/2 there is an additional 10% early distribution penalty and if you are in the 20% tax bracket then you probably should have had 30% withheld or you will owe additional tax.

The 10% you're referring to is probably the early withdrawal penalty.  That's different from the income taxes that you owe on your withdrawal.  

There are a few exceptions that would exempt you from the 10% penalty, but the income tax will still be due.  I'm attaching a TurboTax FAQ that will help explain more.

What are the exceptions to the penalty for an early withdrawal from my 401(K)?