In Italian articles are used in a different way than in English. This is a major difficulty for Italian learners of English, and I suppose it is the same for English learners of Italian :).
Ignoring poetic language (where sometimes the article is omitted or inserted for metric reasons) and other specialized languages (e.g. in telegrams articles are omitted because they are paid by the word), the article in Italian is omitted only in certain fixed contexts. For a detailed list, you can consult this article (in Italian).
In the particular case of general sentences the article can be both omitted and not omitted. So Non feriamo gli animali and Non feriamo animali are both acceptable translations of We do not hurt animals. All the grammars I consulted suggest that the latter (with the article omitted) is a more sustained register, but at least to me it sounds perfectly normal and I wouldn't hesitate to use it in normal conversation.