Why can't we read voltage between just one pin of a loaded capacitor and any ground?
Than I connected the negative probe to any universal ground(earth, a big copper plate etc.) and from common knowledge I know that I could not measure any voltages but I could not understand the physical reason of why.


The voltmeter can only measure the voltage (potential difference) between its two terminals. It doesn't know anything about any other nodes in the circuit.

The capacitor only controls the voltage between its two terminals. It doesn't influence anything about any other nodes in the circuit.

Say you charge the capacitor to 9 V. Then you disconnect the capacitor from ground. The two terminals of the capacitor are still 9 V apart, but there's nothing keeping either one at the the ground potential. Due to a few stray electrons blowing on or off the isolated capacitor due to wind, etc., the potential relative to ground could drift by 10's or 100's of volts.

Then, when you connect the voltmeter like in your 3rd diagram, you provide a path for a small leakage from the top terminal of the capacitor to ground. Now that terminal will end up very close to the ground potential, and the other terminal will end up at -9 V, because the capacitor is still (assuming no leakage through the dielectric) maintaining a 9 V difference between its two terminals.