In a DC circuit, imagine a resistance of 10 Ohms connected parallel to a resistance of 20 Ohms, which is also parallel to a battery of V volts. In such a case, current will be distributed to the two of them.
However, in a short circuit, no current would pass through the resistance. Why does this happen? If the path of electrons is obstructed by the accumulation of electrons at the resistance, shouldn't the same happen in the above case as well?
Your assumption that no current pass through a resistor which has a short-circuit accros its terminals is wrong.
In a realistic circuit, a short-circuit has a non-zero resistance. In that case, the current flowing to each branch depends on the current capacity of the source.
If your source can supply enough current to the short-circuit and the resistor, then both will get the same current as if the other was not there.
Otherwise, both branches will get less current than if the other was not there, but the short-circuit will get way more current than the resistor (KCL will tell you how much).
no current would pass through the resistance. Why does this happen?
The answer from an ideal circuit theory perspective is as follows:
By definition, the voltage across a short-circuit is zero regardless of the current through.
By definition, parallel connected circuit elements have identical voltage across. Thus, a resistor in parallel with a short-circuit has zero volts across.
Finally, by Ohm's law, the current through a resistor with resistance $R \gt 0\,\Omega$ and with zero volts across is zero.
