The step forwards and backwards to the next/previous 'full set' of months makes it difficult for a user to select dates spanning the last month of the current set and the first month of the next set.
Having the 'step' move forwards or backwards by a single row (i.e. three months per step) would solve this problem and be more intuitive for most 'client' users looking to make a booking without overly adding to the time to move through larger time frames.