I can see why "encouragement and bias" might account for higher male achievement, but not why that would at the same time account for lower male achievement.
In a solely encouragement/discouragement based theory, it might be that for some reason, males are encouraged as well as discouraged more strongly than females. I don't know of any (even anecdotal) evidence of this happening, so I wouldn't bet on it.
In any case, the underlying origins of these statistics are no doubt complex, messy and controversial.