There are different kinds of deductions. The tuition and fees deduction is not an itemized deduction. It's what's called an "above-the-line deduction." You can claim the tuition and fees deduction even if you are not using itemized deductions.
There seems to be a part 2 to your question"
Why is a $4000 deduction is better than the $2500 credit?
Not everybody gets the full $2500, if their tax has been reduce to 0. But, with $4000 in expenses, you should get the $1000 refundable AOTC credit if the student is your dependent. So there must be another reason. you're not getting the AOTC.
You can use this IRS tool https://www.irs.gov/help/ita/am-i-eligible-to-claim-an-education-credit