When you dissatisfy someone, you don't meet their expectations. If you promise your dad a chocolate cake for his birthday, giving him a bran muffin instead might dissatisfy him.
To satisfy someone is to fulfill what they need or hope for — and when you dissatisfy them, you fail to do that. Your final research paper might dissatisfy your history professor, and an expensive meal will dissatisfy you if you believe you could cook something even tastier at home. Dissatisfy combines dis-, "do the opposite of," with satisfy, from its Latin root satisfacere, "discharge fully" or "do enough."