The Rambam in Sefer ha'Mitzvos (Lo Ta'aseh #187) explains Rebbi Avahu's logic. He writes that one may not derive benefit from forbidden food because Hana'ah and Achilah are essentially the same thing. Eating forbidden food is one way of deriving benefit from it. This is what Rebbi Avahu means when he says that whenever the Torah says that it is forbidden to eat something, this automatically means that one may not derive benefit from it either, unless the Torah says explicilty that only eating is forbidden.

This may be understood better if we translate "Achilah" with the English word "consume." The Torah prohibits consumption of forbidden foods. Eating is just one way of consumption, so when the Torah forbids eating this really means that the Torah is telling us that one may not consume it in any way.

The Mishneh l'Melech (Hilchos Yesodei ha'Torah 5:8, DH v'Da d'Achar) explains the above idea further. He discusses the prohibition of meat and milk and writes that eating is also considered as benefit. It is as if the Torah would have written, "Do not enjoy meat and milk through any means of benefit, either by eating it or by deriving benefit from it in other ways apart from eating."

The Chidushei Rebbi Akiva Eiger (in Pesachim here) elaborates further and writes that according to Rebbi Avahu, when the Torah states, "Do not eat such and such," this means that the Torah is telling us not to have Hana'ah from eating it. When the Torah writes "Lo Tochal" -- "do not eat" -- this is equivalent to saying "Lo Teheneh b'Achilah" -- "do not derive benefit through eating." The Torah does not mean that it is only the Hana'ah of eating which is forbidden, but rather every Hana'ah is forbidden. The reason why the Torah mentions eating is simply because this is the most common form of Hana'ah.

3) The Sefer ha'Chinuch (Mitzvah #113) adds that the reason why the Torah writes "eating" even though it really means any benefit is that eating is the kind of benefit that a person continually needs.

Kol Tuv,

Dovid Bloom