The Animal Archive talks about intelligent animals taking class levels, and I'm pretty sure the RAI is that normal animals can't take class levels.
I wouldn't allow a non-intelligent animals to take class levels as a GM, so I'd make sure your GM is ok with it.
The "argument from silence" is a poor argument in my book. In fact, I think it's a logical fallacy.
Well, it isn't only an "argument from silence".
1) The bestiary rules (or rather guidelines) for monster advancement has one option of adding class levels. Under the adding class levels section, they mention martial classes as most appropriate for animals (mention amongst others).
Being included here suggest that it is an option.
2) The monster cohort rules have included animals, which specifically are advanced using class levels.
So for this purpose it should definately be possible (albeit the monster cohorts are quite bad compared to a regular PC race cohort).