Voltage Gain decreases when load resistance included

Why does the voltage gain of a (voltage divider) common emitter bypassed emitter bias bjt amplifier decreases when putting a load resistance on the output Vo? I mean Vo should remain the same because resistances in parallel have the same voltage across them. Link below provides the image for the circuit diagram:

Output voltage is $I_C R_L$ and, if $R_L$ halves then voltage gain halves. I believe you are mistakingly thinking that the collector generates a voltage. It doesn't. A BJT is commonly defined as having current gain i.e. Ic/Ib (or hFE). Input current is proportional to input voltage in the circuit above so now you have the transistor with an output current for a given input voltage.
The output current is converted to a voltage by $R_L$ and of course, the lower the value of RL, the lower the output voltage for a given input signal.