No, both you and your parents cannot claim the student loan interest deduction on your tax returns for the loans taken out to pay for your education, given the specific circumstances where you were not their dependent last year. According to the IRS FAQ, your parents cannot claim the deduction for student loan interest on their tax return because you were not their dependent at the time they took out a student loan for you. However, you can claim the deduction with respect to the loan that you took out for yourself, assuming you meet the other requirements for this deduction.
The requirements for claiming the student loan interest deduction, as outlined in Publication 970, Tax Benefits for Education, include that you must have paid interest on a qualified student loan in tax year 2023, you must be legally obligated to pay interest on a qualified student loan, your filing status cannot be married filing separately, and your Modified Adjusted Gross Income (MAGI) must be less than a specified amount which is set annually and is based on your filing status. Since you were not a dependent of your parents last year, only the interest on the loan you are personally responsible for can be considered for the deduction on your tax return, provided you meet the aforementioned conditions.
Sources:
§ 221. Interest on education loans
1040 (2023)
Instructions for Forms 1098-E and 1098-T (2023)
https://www.irs.gov/faqs/itemized-deductions-standard-deduction
Publication 4152 (10/2023)
Publication 970 (2022)
