They were wrong.
For information about Normalize (and Amplify), see: Amplify and Normalize - Audacity Manual
That is called “dynamic range compression” (often just called “compression”, though not to be confused with “data compression” which is used to make files smaller).
Levelling out a range of “whispers” and “screams” requires extreme compression, which will inevitably be fairly low sound quality and there will be a substantial increase in noise when the volume of the whisper is brought up. If you need a “stronger” effect than Chris’s Compressor, you could try this plug-in: AGC - Automatic Gain Control (note that if your tracks are very long, this plug-in will need to be applied to sections of no more than about an hour).