Help me understand capacitor discharging
Why? What is the mistake in my reasoning?


Your mistake is that you defined \$i\$ differently in the two situations. When charging, you defined \$i\$ to be positive when the current flows in the clockwise direction.

When discharging, you defined \$i\$ to be positive when current flows in the counter-clockwise direction.

Whoever came up with the alternate equation for the discharging case didn't do that. Instead they stuck with the same definition with positive \$i\$ in the clockwise direction.

To avoid confusion in the future it would be better to either use a consistent definition for your variables, or give them separate symbols (like \$i_c\$ and \$i_d\$ for the charging and discharging case) when you change the definition.