How can I claim my tuition (1098-T) if it says I can't because my parents could claim it as I'm a dependent, but they don't claim it because I pay it?

If they can claim you as a dependent, they can enter your 1098-T and take an education credit on their tax return.   If you are claimed on someone else's return, you can't take an education credit, so there is no need for you to enter the form.     

It does not matter who pays the tuition and other qualified expenses.  The tuition credit follows the student's dependency. If you are a dependent, your parents are the only ones who can claim the tuition credit (there is a exception, if the student has a large amount of taxable income).

Furthermore, there's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. It is usually best if the parent claims that credit. 

You cannot claim the (up to) $1000 refundable credit if you are, or can be, claimed as a dependent by someone else.

Reference: Line 7 instructions for form 8863.

https://www.irs.gov/instructions/i8863#en_US_2024_publink53002gd0e674

https://www.irs.gov/instructions/i8863