Is it possible, even though rare, that a male in his 20's could have ed?

Rarely: If it occurs at that age, it is more likely psychological than physical. However, one should undergo a medical workup to rule out physical causes.

ED possible: Yes, it is possible for an 25 yo male to have ed though less frequent than in older men. Check with your doc. The causes vary and there may be an easy fix. Docs and psychologist docs see this a lot so no need to be shy. Wishing you health and happiness.