No, being a full time student was not the reason your didn't get a stimulus check in 2020.
As others have said, you will get it in 2021, when you file your 2020 tax return, regardless of the reason, as long as you don't check the box on the 2020 form 1040 that says you can be claimed as a dependent by someone else.
The most likely reason was that that box was checked on either your 2018 or 2019 return, or both. Second most likely reason: you parents claimed you, and you didn't know about it.
"In essence, the stimulus check acts as an advance of your 2020 income tax refund. This means when you prepare your 2020 income tax return, there will be a line to include the section 6428 credit (line 30 on the 2020 form 1040). The credit on your 2020 return is subtracted by any amount received as a stimulus check in 2020. If the amount you received as a stimulus check is less than the credit you are due, the difference will be included as part of your 2020 refund. If you have been overpaid by receiving the stimulus check, however, you will not be required to return any excess amount".
