Learn English – “I entered the classroom during the lesson. Students were paying attention.”

Grammatically, you could drop the and write But these are exceptions rather than the rule.

I think the use of the here is trying to maintain a parallel with the familiar set phrase the exception that proves the rule. This phrase is almost invariably worded with the exception, so omitting the in your sentence makes it sound just a little bit odd.

There are a number of things going on in this question. Having read it over a couple of times together with the additional information in the OP’s comments, I think the best way to approach it is case-by-case.

First though it’s worth mentioning that while the OP has pointed out in a number of comments that the question is not about etiquette, it’s not that simple. When dealing with introductions there are established rules of etiquette that we have been trained to follow, whether we do that consciously or sub-consciously is not important, what is important is that they are there and that they do not always sit comfortably with other ‘normal’ usage.

…this is Tom Smith, our business partner; and this is Jim Blake, our lawyer.

First question – Can we do without the additional ‘this is’?

… this is Tom Smith— our business partner, and Jim Blake— our lawyer.

Generally yes. There are only two exceptions that I can think of; one comes later and the other is where a group is being presented and the person that they are being presented to, often a VIP of some type, makes a comment or asks a question after each name. Think of a royal reception where an elderly Royal makes a politically incorrect statement before moving on to the next embarrassed celebrity. In that case the introduction process resets and you would start again with a ‘This is’

In the same way that I turn to The OED for guidance on etymology and usage, for the definitive guide on matters of etiquette I head to Debrett’s:

Mary, this is Jim Wilson, Bob Aspinall and Sue Godstone.

As an aside, notice that Debrett’s is very keen that you should always make introductions two-way, completing the above example with “Everyone, this is Mary Brett”

Next, this vs these

OK, this is where it gets complicated.

The general rule is that you follow normal rules of grammar – this for individuals, these for groups

This is Mike from accounting

This is my neighbour, john Smith.

These are my classmates, Peter, Paul and Mary

You enter a minefield though when you start dealing with groups that can be thought of as a single entity:

and these are the other band members, Paul, George and Ringo

and this is the rest of the band: Paul, George and Ringo

Are both acceptable.

Finally we come to couples and here all the rules change, or rather, they fall apart. Mary Bryant, a writer on weddings and general etiquette starts with the following:

Couples are introduced separately, although it is advisable to clarify the relationship (‘And this is Sarah, Peter’s wife/girlfriend’).

We’ve gone back to an additional ‘this is’….

However, it is also common practice to introduce a couple as a single entity - The reference found for ‘this is’ in Collins is correct in this instance

This is Mike and Sue Jones who live next door (A couple as a single entity)

Although….

These are our neighbours, Mike and Sue Jones (The same couple, now plural as neighbours)

I started off by saying that we can’t ignore etiquette and I stand by that. But etiquette, like dialect is only another form of usage, another set of rules – confusing and often contradictory.