Nothing requires a parent to claim a dependent, but if they CAN claim the dependent then the person cannot claim them-self - tax law does not allow that. That is why there are two questions "CAN you be claimed by another tax payer?, and WERE you claimed?
Yes to the first means you cannot claim yourself, no to the second might allow you to claim certain educational credits that usually only the person claiming you could claim.
Q. Is it possible to Claim 1098-T in student taxes filing, when parents are not claiming as dependent in their taxes?
A. Theoretically yes, even if parents paid for Tuition and fees. But, from a practical point, the answer is no.
While technically there is a provision that allows you to claim a tuition credit, from a practical matter it seldom works out. A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit if he/she supports himself by working . She cannot be supporting herself on student loans & grants and 529 plans and parental support. It is usually best if the parent claims that credit.
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return.