There are various reasons to have character limits for tags, and more than a few downsides.
This is a major reason. Let’s say you raised the tag character limit to 50 characters.
Then you could have tags like blahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh . As you can see, this already takes up nearly half a line. So while four 25-character tag names (a rather uncommon use-case) can more-or-less fit comfortably on a line, two 50-character tag names (probably a more common situation) take up the same space. Many lines of tags can look pretty ugly. And anything over about 100 characters is simply right out the window, since it would have to be split over two lines.
There is also a problem with readability. Tag text is in a smaller font, and displayed on a gray background, which makes it a lot harder to read even for short tags. Tags that are fifty characters long could be atrocious.
On a related note, this might also increase the likelihood of spelling errors in tag names, as well as decreasing the likelihood that anyone would spot them.
On programming sites, as hinted at in this post, long tags often tend to be the sorts of things that can (or even should) be broken into smaller pieces, which is to say, one that is too specific. For example, instead of excel-spreadsheets-in-windows-10, try using excel, spreadsheets, windows-10 (this is not actually SO’s usage guidance, but rather an example).
Such concerns are basically why there is a 25-character tag limit.
In fairness, though, there are some serious downsides as well, which bear consideration. Some are also more specific to our site and a few others, rather than SO and the other programming sites, where this size constraint likely originated.
In many cases, we simply need longer tags, since they arise naturally from what the site considers. The specificity concern does not hold, since miss-peregrines-home-for-peculiar-children (which does not exist, since it is too long) is not in any sense more specific than aftermath, nor could it meaningfully be broken into miss-peregrine, home-for-peculiar and children.
The general solution to the problems mentioned previously has been to use a smaller but still meaningful subset of words. Frequently, however, this defeats one of the primary purposes of a tag, searchability. The problem is even worse on certain sites, such as Anime, where anime, manga, and light novel names tend to be quite long.
The only solutions at this time are to choose a smaller set of related words, or use an abbreviation. Neither one of these is ideal. The second might work better with some series that have a commonly accepted abbreviation, but is downright ugly with others. Does anyone really want to see mphfpc instead of miss-peregrines-home-for-peculiar-children?