Why does the Embraer E-Jet Family have doors of different sizes?
It's actually more common than one might expect, and not just in the E-jet family.

The de-facto standard is that passengers board from the left and the right side doors are only used to load logistical stuff (ie catering) during the turnaround or during an emergency evacuation.

As such, the left side door(s) must fit certain FAA standards (so it fits jet bridges or the average human height, for example).

For example, on the Boeing 737 (all models), the left forward door is 0.86 x 1.83 meters while the right forward door is 0.76 x 1.65 meters, 20 percent smaller (by area).

Now you might ask "ok, so make both doors the size of the left door". It's beneficial, from engineering/structural point-of-view, to have each door as small as possible. 

(http://www.boeing.com/assets/pdf/commercial/airports/acaps/737.pdf pages 73 and 77)