Why do we need "dengan"? I got answers from native speakers! For more information, please refer to the post on HiNative. https://hinative.com/questions/18242444
Although their answers are not so clear, I'll try my best to explain.
You can NOT drop "dengan" in this context because this sentence describes her preference for SPECIFIC occasions from an objective perspective. If she doesn't like me as a whole human being, you can say "dia tidak suka saya" (i.e. drop "dengan" from suka) though.
Quoting from the answer from the native speaker on HiNative:
[NG] Saya suka dengan sepatu. / I love shoes.
[OK] Saya suka dengan sepatu ini / I love these shoes.
"Dengan" is required to pinpoint "these" shoes. "Suka dengan" + general concepts makes native speakers wonder "what kind of thing???"