Yes actually I agree. I read that da + lo stays as "dallo". Besides it's not "lo animale". It's "l' animale". dall' comes from da + l' indeed. I think this table is helpful: http://italian.about.com/library/fare/blfare153a.htm
In leggo all'uomo the preposition is 'a' not 'da' ;)
You're perhaps thinking of cases such as "Vengo da te" (I come to you), but in that case 'da te' means "where you live" rather than identifying 'you' as a destination; for instance you'd say "Da me manca la corrente" (In my home there's a power outage) without implying movement.
Try not to focus on the association between prepositions in the two languages; they're often used for different purposes and in most cases you can't assume a direct equivalence.