We file Married filling Jointly and both of us are claiming 0 deductions with minimal dividend income or any other financial gains. So why do we owe taxes?

[Bsch4477]

We can’t see your return but you owe tax when your tax liability is greater than tax withheld. 

[SweetieJean]

That is common when both spouse work.  You can end up in a higher Joint tax bracket than either of you are individually (and no, filing Married Separately won't help.).

But you can mark your W-4 forms as "Married, but Withhold at Higher Single Rate," and/or have flat amounts of additional dollars withheld.