For small applications, I'd recommend agile methodologies such as XP, AUP or MSF Agile, depending on the team's knowledge and the application at hand. For example if your desktop application being developed using Microsoft's technologies, MSF Agile would be better. For Java-based development  I'd rather go with XP / AUP. (Although I don't have practical experience with AUP)

It's obvious that heavy-weight processes such as RUP are not recommended, because the work required to deploy the process  itself would exceed the work required for the application itself.

Anyway, choosing the process for small applications is highly dependent on the team and its knowledge. Maybe your instructor was assuming that the typical team can be adapted to SDLC easier. This can be the case for a typical, non-professional team, because understanding and adaptation to the process requires less experience and learning. (Maybe!)

Anyway, I don't agree with your instructor.