Angle CAD can be equal to angle CBE. If angles CAD and CBE are not equal, then we can choose a point A' on AD so that angle CA'D is equal to CBE. So we can move point A to A', and then angles CAD and CBE will be equal.
Nice answer guest, but I don't think it's correct. Here's why:
Since AD is parallel to BE, Angle BEC = Angle ADC, and therefore, in order for Angle CAD to equal angle CBE, triangles BEC and ADC must be similar to each other. That can only happen if angle BCE = angle ACD, and that can only happen if A is on BC. Since that isn't allowed, angle CAD cannot be equal to angle CBE.