If I live in Kentucky and work in Kentucky and Ohio why do I owe so much in Kentucky state taxes?

It depends.

Typically, if you owe taxes, you may have earned more income than you did in prior years or did not have enough withholdings or estimated tax payments made during the year to cover the total taxes due for the year.  Please see this link for more reasons as to why you may owe more in taxes than your anticipated.  

Also, I would recommend reviewing your input.  Since Kentucky and Ohio have state reciprocity, you should not have any wages taxed within Ohio.  Essentially, states with reciprocity agreements agree to only tax the taxpayer in their resident state and will not withhold taxes on the nonresident state.  Please see this link for more information.  If you determine you do have wages that are also being taxed and have withholdings in Ohio, you will need to fill out form IT-4NR and submit it to your employer so they only report your wages as being from Kentucky.

Finally, if you determine you are required to file both Kentucky resident and Ohio nonresident returns because your employer reported both states on your W-2 forms, be sure to complete the Ohio nonresident return first.  This will ensure Kentucky picks up a state tax credit for any income also taxed in Ohio and will provide you with a credit on your Kentucky tax return.  This will help reduce your Kentucky tax liability as a credit is a dollar for dollar reduction in your tax liability.  Please see this link for more guidance on how to prepare these returns in TurboTax.