I'd suggest to study this glossary.

line organization
An organization in which there are direct
two-way lines of responsibility, authority, and communication running
from the top to the bottom and back to the top of the organization,
with every employee reporting to only one specific supervisor.

line personnel
Employees who perform functions that
contribute directly to the primary goals of the organization.

staff personnel
Employees who perform functions that advise and assist line personnel
in achieving their goals.

In a system that makes such hazy terminology as "junior executive" psychologically necessary, they are of the staff as much as the line, and most are destined to live poised in a middle area that still awaits a satisfactory euphemism."

Without full context of the article it is difficult to say, but my interpretation would be with Aperisic, that 'the line' here refers to the factory production line. The point being that although they feel they have a better job and a more important position, actually they are still very minor and unimportant parts of the company. They shouldn't consider themselves above those on the factory floor and they have no more prospects of promotion or advancement than those operating the machinery.
William H. Whyte, Jr. wrote:

"This book is about th organization man. If the term is vague, it is because I can think of no other way to describe the people I am talking about. (...) These people only work for The Organization. (...) They are the ones of our middle class who left home, spiritually as well as physically, to take the vows of organization life, and it is they who are the mind and soul of our great self-perpetuating institutions. Only a few are top managers or ever will be.

In a system that makes such imprecise terminology as "junior executive", although it could be psychologically needed to use that terminology, the people of middle class (mentioned above) are the ones who belong to the staff as much as to the line of production (they manage results and they produce results), and most of them cannot avoid to live balanced within a (certain almost undefined) middle area that is still waiting a satisfactory less offensive synonym (than I guess middle-class)EndFragment>
Students: We have free audio pronunciation exercises.
 nona the brit's reply was promoted to an answer.
Hi Cadzao,

It's nice to see you in the Forum, I hope that you find it useful and enjoyable.

Best wishes, Clive
Clive, so good to see you again in the Forum.

Site Hint: Check out our list of pronunciation videos.