What determines handedness of wind circulation around pressure extrema in the atmosphere? I'm reading a textbook (Atmospheric Science - An Introductory Survey 2nd ed, John M. Wallace • Peter V. Hobbs) which states (p14):

The winds observed in the Earth’s atmosphere closely parallel the isobars. In the northern hemisphere, lower pressure lies to the left of the wind (looking downstream) and higher pressure to the right. It follows that air circulates counter-clockwise around lows and clockwise around highs.

What is the reasoning here - I can't find a reason for handedness in the assumptions.
 A: In the northern hemisphere the Coriolis effect tends to deflect a moving mass to the right. (Consider your velocity relative to the surface of the earth when going to the north or south.) Air tends to flow toward a region of low pressure.  If is deflected to the right it ends up going counter-clockwise around the low (and clockwise while leaving a high).
A: If you were to start a system from rest with, say, a low-pressure region in the middle, the initial movement would indeed be from the outer area toward the middle.  As the flow accelerated, the Coriolis force would begin to curve the trajectories toward the right (in the northern hemisphere).  The flow would continue to evolve until it reached a stable state: one in which the sum of the forces felt by a fluid parcel is just the force needed to keep it in a repeating orbit.  At that point, the flow would persist.
So, when the combined force due to pressure gradient (inward) and Coriolis (to the right, which for a circular trajectory is outward) provides the right amount of centripetal acceleration to keep the fluid parcels moving in circles around the low pressure center, that swirling motion is going to last for a while.
Of course, the atmosphere doesn't do this ideal experiment--the air is moving all the time and never starts up from a standstill.  But nonetheless, flow around high- or low-pressure regions tends to approach a stable circulation, which is why it's very common to see flows like this.
