Troubling understanding simple diode circuit
I can't understand the affirmation that Vd can't be positive... Where does that come from?


Because the diode is only "off" when Vd is negative. So if you find that Vd is positive, it contradicts your initial assumption that the diode is off.

In the comments you asked,


  So I can't get a voltage increase through a resistor?


You can, but only in proportion to the current through it. Since you assumed the diode is "off", there is no current flowing through the diode. Then, by KCL, there is no current flowing through the resistor. So, by Ohm's law, the voltage across the resistor must be 0.