As a native speaker I sort of agree, though it would sound more natural to say it with a descriptive word; -
"I am cooking soup" or "I am cooking a tasty soup".
"I am cooking 'a' soup" sounds wanting of a description, for example, "I am moving A soil" sounds wanting, such as, "I am moving a lot of soil"
If the soup is specific, it needs specifying, otherwise it's more natural to avoid the particle in the sentence.
Fixing can be used to describe making food, however it's much more informal and uncommonly used by most people. It also sounds specifically very American to my British ears. However, it is still understood by everyone with context.
It should only be noted that 'fixing' is not interchangeable with 'making'.
For example, 'making a bike' and 'fixing a bike' have two very different meanings.