Why do I owe tax to the state of Illinois if the state of Illinois does not tax active duty military pay

Likely there is other income showing up for IL.  You can view your IL tax summary using the steps below to help you locate the income source.  There may be some income from other sources such as interest or dividends.  Additionally, there is some military pay that you cannot subtract from IL.  

Here is an extract from IL Publication 102.  

" You may not subtract military income (such as combat pay) that you excluded from your AGI on Form IL-1040, Line 1; 

pay you received under the Voluntary Separation Incentive; 

pay you received from the military as a civilian; 

payments you made under the Ready Reserve Mobilization Income Insurance Program; 

or pay for duty as an officer in the Public Health Service."

1. Select "Tax Tools" in the left hand menu
2. Select "Tools"
3. Select "View Tax Summary"
4. Select "Preview My 1040" in the left hand menu

5. Select "IL Tax Summary"