The reason is that Illinois property taxes are assessed "in arrears." That means the taxes you pay in 2017 are for the year 2016. Since you did not own the property in 2016, you are not entitled to the credit for those taxes. Most likely the home's seller gave you a credit for those taxes at closing, because you would be the one actually making the payment. Therefore in effect the seller actually paid the taxes. You can check your closing statement to be certain.
When a home is sold, the seller is responsible for the property taxes up to, but not including, the date of closing. The buyer is responsible for the property taxes from the date of closing forward.
From the Instructions for Illinois Form ICR:
"You may not take a credit for taxes you paid if the seller reimbursed you at the time of closing. You also may not take a credit on your 2017 return for property you purchased in 2017."
http://www.revenue.state.il.us/taxforms/IncmCurrentYear/Individual/IL-1040-Schedule-ICR-Instr.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
