My husband lives in IN and works in KY. His w2 only states he pays IN state tax as is the state agreement. Why does KY say we owe money?

You should not be filing a KY return at all.  IN and KY have reciprocity.  This means, whatever you earn in KY while a resident of IN, is only taxed by IN and vice versa.  

You will simply need to delete your KY return and only file  your IN resident return.

In the personal info section, when it asks if you made money in another state, answer NO, per the reciprocal state instructions, on that page. This will prevent TurboTax from thinking you need to file a KY return.

The reciprocity agreement does not apply to KY city and county taxes (box 19 of the W-2).  You can not get those refunded.

Most  IN counties (but not the state)  allow a credit, or partial credit for tax paid to a KY city or county. That will come up in the IN state interview.