First, it is actually not true that an expression containing NULL evaluates to FALSE.

It evaluates to UNKNOWN.

A WHERE clause filters out all UKNOWN values, and that is why you get this behaviour in your first query.

But not all SQL constructs filter out unknown values so it will give confusion to people if you tell them that expressions with NULL in them evaluate to FALSE.

If I had to teach your students, I would also tell them to never add any condition into the ON clause which is not a direct join relation between the tables (i.e. table1.column1 = table2.column2). This helps them understand the proper purposes of the ON versus the WHERE clauses. (In your final "correct" query you added such a condition).

Rather have them understand why the WHERE clause does this (filtering UNKNOWN values).

Otherwise I recommend the book from Itzik Ben-Gan "T-SQL Fundamentals" which covers the above.)

(Interestingly, he writes in that book that it is the most difficult task to write about the "simple" basics - and it is ...)

Second, I would add that there is another confusion which specifically arises with LEFT OUTER joins, which I believe is even more common with SQL beginners:

If you, in your example, simply wanted to get a list of professors, and also list if they had any class at all, you "naturally" would think "we'll use a left outer join, this will return a list of all professors, and it will list the class he has and if he has no class it will be null on the right side".

And then they are confused as to why it does not return a single line with each professors, but there are several rows for a single professor (if he has more than one class).

So the description of a left outer join as "it returns all rows of the left-hand table, even if there is no row in the right-hand table" is very misleading - it can be understood to imply it would return exactly the rows of the left-hand table, plus data from a matching row if there is one.

But that is not what it does.

In fact, what it does is: join all matching rows from both tables (inner join), resulting in potentially many "duplicate" rows from the left-hand table, and then add a single row for all left-hand table rows which have no matching equivalent in the right-hand table.