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.
See https://www.irs.gov/Individuals/AOTC
https://turbotax.intuit.com/tax-tips/college-and-education/what-is-the-american-opportunity-tax-cred...
https://ttlc.intuit.com/community/credits-and-deductions/help/who-is-eligible-to-take-the-american-o...
You can use this IRS tool https://www.irs.gov/help/ita/am-i-eligible-to-claim-an-education-credit
