The hangup seems to be "sailing toward the pre-start side of the starting line" is different from "sailing toward the starting line." Sailing toward the pre-start side implies that the boat is not on the pre-start side.

Aldo

I think the phrase "pre-start side of the starting line" is intended to refer to the entire area that is on the pre-start side of the line, and not just that side of the line itself (i.e. not just a 1mm strip on the pre-start side of the line). A boat that is already on the pre-start side of the line is therefore not sailing "towards the pre-start side of the starting line" (irrespective of which direction they are sailing in) since they are already on the pre-start side of the line. Only a boat that is on the course side of the line and sailing back towards the line (or one of its extensions) is sailing "towards the pre-start side of the starting line or one of its extensions".

Note that boats that have started early do not have to return through the line, they can equally well go round an end (and indeed are required to do so if rule 30.1 is in force). The reference to a boat "sailing towards the pre-start side of ... one of its extensions" means that rule 22.1/21.1 applies equally to boats returning round an end as it does to boats returning through the line itself.

Aldo, if you read about half way through this thread, you'll see a discussion of some of these terms and their possible interpretations (with drawings too).

https://www.racingrulesofsailing.org/posts/501-ocs-around-the-pin-end

or

Ang

I see Aldo's point: a line is a two-dimensional object defined by just two points. The side of an object is the edge of an object, not the region around the object. For instance, edge of a circle is equivalent to its circumference, not some unspecified region around the circle.

In a traditional start with an initial weather leg, the pre-start side of a two-dimensional line is immediately to leeward of it, and yes, all boats starting properly are sailing towards the pre-start side as Aldo says.

The arguments above are implying that lines have a third dimension, which of course they don't. That flies in the face of geometry going back to Euclid.

It's too late for the 2021-24 edition of the rules, but perhaps in the next edition, new definitions could be added for "prestart zone" and "course zone". A zone is, of course a three-dimensional object, and we already use the term "zone" when discussing mark-room in Rule 18.

We all know what the rules intend, but to me, it seems like Aldo's found an inaccuracy in the wording of the racing rules that should be fixed.

I think Aldo explained it and Ange's drawings showed it. It cleared it up for me.
Con

Considering the wooden fence between my house and my neighbor's, if I keep to "my side" of the fence I will end up with splinters.
Edit:  THAT WAS SARCASM!
In fact my two dimensional property and my three dimensional house are all on "my side" of the property line.
One can walk "from the neighbor's side to my side" of the property line. The mailman does it every day and never gets confused.

Al, 
If you think about the USA - Mexico border, it is a line where the two countries meet.  If you are in Mexico, you are on the south side of the border line.  If you are in the U.S.A., you are on the north side of the border line. 
Same for a start line.  There is an area which is on the pre-start side and an area on the  course side of the line.

With respect to Al, a point has 0 dimensions, a line has 1 dimension (length) and an area has 2 dimensions (length & width).  You cannot be sailing towards the "side of a line" as the line itself has no "side".  A straight line divides a plane (the surface of the ocean) into two areas.  In our case we call one the prestart side and the other the course side.  I guess they could write the rule as saying you are sailing towards the prestart area instead of the prestart side of the line to be absolutely correct but I am not sure that adds to the understanding of the rule.

Thinking about this further, I think the issue is that "side" has multiple meanings:

1) The edge of something, as in "a rectangle is a four SIDEd polygon".
2) A region adjacent to an object, such as "the American SIDE of the border"

Aldo, Philip, and I (initially) seem to be thinking only of the first definition above.

Murray, Carl, Graham, and Angelo seem to be referring to the second definition.

I understand this isn't the place to submit suggested wording changes (how does one even do that?) but for the next edition of the rules ('25-'28), it might be worth changing "side" to region so the definition isn't ambiguous.

So, new rule 21.1 would become (change in CAPS):

"A boat sailing towards the pre-start REGION of the starting line or one of its extensions after her starting signal to start or to comply with rule 30.1"

Thoughts?

First of all, the full rule 21.1 is:
21 STARTING ERRORS; TAKING PENALTIES; BACKING A SAIL
21.1 A boat sailing towards the pre-start side of the starting line or one of its extensions after her starting signal to start or to comply with rule
30.1 shall keep clear of a boat not doing so until her hull is completely on the pre-start side.

and the definition of Start: A boat starts when, her hull having been entirely on the pre-start side of the starting line at or after her starting signal, and having complied with rule 30.1 if it applies, any part of her hull crosses the starting line from the pre-start side to the course side.

Based on Merriam Webster's 2nd definition:
2 : a place, space, or direction with respect to a center or to a line of division (as of an aisle, river, or street)

We don't say we are going to/towards the "right region of the room" we say - we are going to/towards the "right side of the room" which implies we are going to be on right of the imaginary center of the room from some place that is not the right side of the room.
So if we are "sailing towards the pre-start side of the starting line" we will be heading towards the space or in the direction of the pre-start side of the line which implies that the boat is not on the pre-start side of the line when it starts heading that way. I think that it is implied but not explicitly stated that the boat is OCS that is possibly confusing.

Thus, to clarify the intent of the rule to remove any ambiguity, I would suggest reverse mirroring the definition of START to remove the ambiguity and insert the phrase FROM THE COURSE SIDE as follows:
21.1 A boat sailing  FROM THE COURSE SIDE towards the pre-start side of the starting line or one of its extensions after her starting signal to start or to comply with rule 30.1 shall keep clear of a boat not doing so until her hull is completely on the pre-start side."

You would have to be 15,000 miles away on the opposite side of the planet for that wording to make a difference. 
The present wording is clear.