Subject: How does wind appear to blow between centers of high and low pressure?

I researched my answer on the web using multiple search engines since my 
science book didn't have anything on meterology. The references I found told me 
that the wind around a high pressure system goes clockwise and the wind around 
a low pressure system goes counter-clockwise.  Thus, if the high pressure 
system on the map is on the left (west) and the low pressure system on the map 
is on the right (east) I reasoned that the wind at the middle between the two 
systems would go from the top down.  My teacher says that isn't so but won't 
explain what happens and I'm trying to make sense of what goes on with the 
winds.  I'd appreciate any help you can provide about how the wind blows 
between centers of high and low pressure.  

Re: How does wind appear to blow between centers of high and low pressure?