Most studios have showcases of some kind, I think, but I've never heard of forcing students to perform with no advance notice!
Personally, I do find having the goal of a performance or competition does help me focus and stay motivated to work hard on my dancing.
But if you don't want to, you shouldn't be pressured. Have you been at the same studio for 5 years? If so, you're good customers! I've been with the same instructor and studio for 4 years and I know they appreciate me. Put your foot down and let them know that's not for you and that you find being pressured unpleasant. Are there any other studios in your area?