If every complaint on here about lazy students were justified, humanity would never have made it this far.
There are many explanations for the response you describe and thinking of your students as lazy or entitled is about the least productive one. Sure, you didn't use those words, but it shows in your answer that you think the problem is with your students' attitude, and not in your approach to the material. Whether this is true or not, it shuts down any avenue to a productive solution.
Consider the possibility that your students are communicating a genuine concern and being frustrated by your unwillingness to change anything. Sure, you don't want to give away the answer, and the students don't feel like they can get there with what they're given and no further instruction. What makes you think those are the only two options?
Imagine being taught improvisational piano playing, having no background in the piano whatsoever. You ask the teacher to tell you which keys to press. The teacher tells you, no, that's not what we do here. You can learn to play music somebody else has written down the hall. Here, you learn to improvise. Now play.
This might help you to understand your students' frustration. Just because your teacher doesn't want to tell you which music to play, doesn't mean he can't help you figure out how to do it.
You ask for which keys to press because you don't know any better. It's not the right question, but you're the student. How are you supposed to know where to start?
The truth is that there are plenty of other things to try, but it's the teacher's job to come up with them.
- The teacher could play something himself and describe what choices he's making.
- You could watch some great improvisers play and discuss what they are doing.
- The teacher could explain some basic chords and progressions that help with improvisation.
- The teacher could allow you to copy a few simple improvisations, just to help you get familiar with the piano. So long as you both understand that this is only part of the process.
- The teacher could design a curriculum from simple improvisation to more difficult so that each step seems manageable.
All this, the teacher can do to help you learn how to improvise. Just because some of these exercises are not full improvisation, doesn't change the end goal. It's just a matter of finding the right training wheels.
Most likely, this is what your students are telling you. They don't want you to tell them the answer, they want you to meet them half-way.
Maybe not. Maybe these students are really just lazy and entitled. But once you draw that conclusion, the battle is lost, so you might as well start with the interpretation that they are trying to communicate a legitimate frustration.