Different reviewers have different standards, much like different editors have different standards. There are more potential sources of edits than reviewers however, so the reviewers have to win. Outside of automatic audits, there is no system for reviewing the reviewers because that simply gets too meta.
What follows is purely opinion, nothing concrete, but there are a few generalizations that apply here:
All edits to ancient posts are suspect. Edits bump a topic back to the front page. The longer it's been since an edit, particularly if the Q&A has run its course, the more likely it is that the edit will be rejected.
Style varies from person to person. Edits that split hairs on preferences in presentation style are likely to be rejected, particularly when editing an ancient post. Your attempt to segment the answer into headings falls into this category. That was not the only change it was making, but...
The meat of your edit should not be a comment. When the iffy parts are pruned away, if the only surviving material would have done well on its own as a comment to the post that is being edited, then it's probably best to lean in the direction of a reject.
Low rep bias. The less time you've spent contributing to the site, the less inclined people are to give you leeway with edits they consider borderline. That's just human nature, and not specific to any individual Stack Exchange site.
The post was old enough and the answer already clear enough that it did not warrant the edit
You actually added content to the answer to clarify and/or further explain the answer - while the content you added was indeed good and valuable, it wasn't part of the original post's answer which, in my mind, makes an edit invalid. You should add that additional content either as a comment to the answer or an additional answer.
Iain was trying to be non-judgmental in his answer, so I won't be...
The answer to the question you asked in the first comment is: no, edits that improve answers aren't necessarily rejected because they aren't required, but your edit was rejected because it didn't improve the answer. It was a bad edit and deserved to be rejected.
It didn't make an overall improvement to the answer. I thought one part of the answer was somewhat clearer after your edit, but most of it was not improved.
It made the answer harder to read. The large headings were jarring and didn't add improve the readability of the answer.
As Iain has said, the other 4 canned reject reasons don't really cover this situation, but typing a custom reason takes a significant amount of time, so picking "invalid edit" is a good compromise for a reviewer.
Everything stated in the other answers can be summarized as:
(primary) The edit was controversial at best and a degradation at worst. This alone is enough of a reason.
The edit was to an old and high-rated answer. So, it must be on par with its perceived quality (which is proportional to both these parameters) which it isn't.
It requires the site's reviewers to invest some time. As they're mostly professionals, they generally wish the edit to be worth their time (to avoid attracting ever more "unworthy" ones and be spending ever more time on them).
This actually means to have big enough value/time to review ratio. So, you can
increase its contributive value (make it more "substantial"), and/or
make the improvement more obvious (by any means, including edit summary) to decrease the time required for a "passer-by" to understand:
the essence of the change, and
how it serves the purpose of the original post.
Note, however, that you cannot decrease the time beyond what is spent on bringing up the review screen and taking a glimpse of it.