If I paid state tax to IN for 11 months, and state tax to MI for 1 month, why is IN saying I owe them more in taxes when Turbo Tax said I was getting an IN return?

It depends on where you lived and worked in 2022 and how you entered the information in TurboTax.  IN and MI have a tax reciprocity agreement.  That agreement says only your resident state will tax your income even if earned in the other state.  So if you lived in IN all year but worked in MI and there was MI tax withholding you would've needed to file nonresident for MI and allocate zero income to MI to get the taxes refunded.  You would owe tax to IN for all the income. You would not get a credit on your IN return for taxes paid to MI as those were refunded by MI.  

If you actually moved from one of the states to the other then you would file part-year returns in each state an allocate the income based on when you were resident in each state. There would also not be a credit for taxes paid to another state on either state return. 

IN should explain in your correspondence how they arrived at their decision and refer you to the IN form location for the changes. IN is likely having your return part of your refund because all of your income should have been taxable in IN with no credit for the MI tax due to the reciprocity agreement.  

We cannot see your return in this forum.  You may need to repost here with how you filed in each state and what IN is saying is being changed for more specific interpretation help.