Why do we need to strain the juices? Isn't it better to have them with all the fiber?

Although fiber is excellent, we remove it while making juice because processing fibre wakes up your intestines, and requires them to start working. 

However, we suggest drinking juice in the morning in order to support your cleansing, continuing to give your intestines a rest. The purpose of removing the fibre is to make the drink  easily digestible for your body, and to keep continue giving your organs rest. On the other hand, an unstrained juice would requite slightly more digestive energy to be processed.