why "zij steunt mij niet" is wrong?
I'm not sure which exercise you had, but "zij steunt mij niet" is also correct Dutch.
Well, I had the Dutch-English translation exercise, and it said "Zij steunt ME niet."
Look it up in the grammar rules.
If you emphasise "me" it changes to "mij" in this sentence
I had this as a listening exercise in which the voice did say "je" rather than "jij". Maybe the same for you? If it was a writing translation exercise though, of course your suggestion should also be correct.
Why it's not "They don't support me?"
That'd be zij steunen, as opposed to zij steunt.