広辞苑（A Japanese dictionary)
でぶ 肥えていること、また、その人をあざけっていう 語
Hi. I think every Japanese native knows the word.
It is not slang, but colloquial and a dirty-word, like "fat-ass".
I strongly believe that your teacher misunderstood what you said,
or he/she pretended to not-knowing, because he/she didn't want you to learn a dirty-Japanese-word.
Oh, you're asking the etymology?
Sorry. I don't know.
edit) The mighty Wikipedia says that it comes from the adjective でっぷり.
In Edo-era, でっぷり became でぶでぶ, then became でぶ.
デブ - Wikipedia