Why is the Sun called an "average star"?

Describing the sun as an average star is probably more of a reaction against the idea that there is something unique about it. Obviously there is for us, since it is the star that we happen to be in orbit around, and much closer to than any other star, and hence historically the sun has been considered rather unique. But over the centuries we've discovered that neither the sun nor the earth is the center of the universe, that the stars we see in the night sky are just like our own sun, and that some of them are much brighter and/or much larger (in mass or volume).

So saying the sun is an average star is mostly a historical artifact. It is saying that we've discovered that there is nothing particularly unusual about our star compared to any other star in our galaxy.

It isn't a claim that the sun is average in any particular mathematical sense. It is using 'average' in the sense of 'typical' or 'unexceptional'. As it happens, it turns out the majority of stars are in fact smaller and less luminous than our sun, so it is somewhat un-average in that sense.

Why is the Sun called an “average star”?

The sun is a yellow dwarf star and dwarf stars are the most common in the universe. Technically, the sun's spectrum peaks in the range of green light, but we see it as effectively white.

I am inclined to think if an astronomer or physicist told you the sun was "average" it is because it is part of the main sequence line of the Hertzsprung–Russell diagram (see below).

Most of the stars on this line are classified as dwarf stars.

...about 75% of the stars in the universe are red dwarfs, which greatly differ from the sun.

I am not sure greatly is the best word. Yes red dwarfs are generally cooler, less massive, and their interiors dominated by convection, but by appearance alone their differences are not all that great.

I've tried doing a little bit of research and I've found that the sun is "average" if you exclude all the dwarf stars from you calculations.

By all the dwarf stars do you mean orange, yellow, red, white, and brown dwarfs, etc.? If you eliminate all of these except for the sun, then the sun would be extremely odd.

Is there a good reason why this is done?

I am not sure what you did exactly, but I think you may have misunderstood what was meant by "average" (see my comments above).

As a followup to @honeste_vivere's note about the H-R diagram, our sun really is living in the middle of average-town:

The image, from Wikipedia plots 22,000 stars. When you plot a star's temperature vs brightness, they seem to follow certain patterns.

Our star lies right in the middle of the boring main sequence.