I'm confused

In a military history book I'm reading is the following quote, one I don't fully understand. It rationalizes the failure to secure an area on the flank of the advance, saying.  ". . . there are security advantages to be gained from having a dangling flank curve behind an advancing front line; it prevent[s] the enemy from rolling up behind the advancing front line." How is that the case? By leaving the flank occupied by the enemy and pushing forward, isn't the enemy (by definition) already behind your line of advancement?  If you know, please explain.

If you're tactics are highly stressful, then your enemy will be driven before your line of advance, or destroyed by it.  Enemies behind your line of advance result from imperfections in, or the failure of your tactics.  - Fred

Sure, but the author was arguing that leaving the enemy on the flank - in this case - helped secure the rear of the advance. I do not see the logic involved. - Me

With forces on the flank, the enemy is prevented from sending troops in a circular maneuver to come at the rear from an oblique angle. - Fred

update: I wrote the author of that military quote (Eric Hammel) and asked him to explain. Here's what he wrote back: 

It's difficult in 2012 to know exaclty what I was thinking in 1991, but it seems to me now that I had had a line described to me that looked like this (taking into account the limitations of keyboard symbols:

  ^^^^^^^^^^^^^^

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It would prevent--or at least constrain--an enemy force from rolling up the (in this case) left flank in detail from left to right.

If I'm not mistaken, Patton's right flank was open during the September 1944 part of the advance across France, but XIX Tactical Air Command "dangled" on that side of Third Army and thus provided that sort of flank protection.