As per my understanding, all adiabatic processes carried out in absence of an adiabatic wall need to be fast enough so that there is no heat exchange with the surrounding. Similarly, all isothermal processes are slow so that thermal equilibrium can be established with the surroundings in order to maintain a constant temperature in the system.

But then since isothermal processes are slow, how are isothermal irreversible processes possible?

Is my notion that 'irreversible processes are fast' wrong?