Is the F test used for testing the difference in two population variances always a one tailed test? Why or why not?
Yes, it is always one-tailed.
The specific "F-distribution" is a skewed curve from which we are trying to determine whether the "F-value" we obtained from our variance comparison is 'random' or not. That is, does it reject my Null Hypothesis or not?
For a useful discussion and graphical examples, see: