Here's why:
* "Dilemma" is a noun, meaning a situation in which a difficult choice has to be made.
* "In dilemma" is not a grammatically correct phrase. You wouldn't say "in happiness" or "in sadness" either.
* "Having a dilemma" is a common and correct way to express the experience of being in a difficult situation.
Example:
"I know you're going through a tough time right now. It sounds like you are having a dilemma."