Why would I need a third table in a one-to-many relationship?
I don't know what your professor has really said I am not sure if I understand your model. But maybe the following is interesting.

In the article A Logical Design Methodology for Relational Databases
Using the Extended Entity-Relationship Model by T.J Teory, D. Yang and J.P. Fry is described how entity relationship diagrams can be transformed to relations (and tables). In Fig.8f (on the p 13 of the pdf) there is the following example for an 1:n relationship:


  Each engineer can have at most one
  secretary. One secretary could work
  for several engineers.


There is a relationship "works-for" between the entities "secreatry" and "engineer". 


A "secretary" "works-for" an "engineer".
Each "engineer" has at most one "secretary" that "works-for" her. It may be that an "engineer" has not "secretary" that "works-for" her. 
A "secretary" can "work-for" one, more or no "engeneer"


In the article the authors propose to represent this as

ENGINEER(*EMP-NO,...,SEC-EMP-NO)
SECRETAY(*EMP-NO,...)


the fields marked by * are keys. The field SEC-EMP-NO referenes a EMP-NO from SECRETARY and is nullabel.

But there are authors that have the opinon that null values should not be allowed in relations. If one wants to avoid null values one needs a third relation to create the following model:

ENGINEER(*EMP-NO,...)
SECRETAY(*EMP-NO,...)
WORKS-FOR(*ENG-EMP-NO,SEC-EMP-NO)


ENG-EMP-NO references an EMP-NO in ENGINEER and SEC-EMP-NO references an EMP-NO in SECRETARY.

If an "engineer" always has a "secretary" that "works-for" her then the first representation with two relations does not contain null values.

Edit:
I now found the comment in your post that links to the diagrams (http://i.imgur.com/gIG2D3h.jpg)  of your professor: Actually he introduces a third table  to avoid null values as described here.