Two main reasons: first, the categories I've been removing have never actually been created. Pages have been linked to those categories, but if you go to the category page it doesn't exist (it has no introduction, it isn't in any other categories, and you get the wiki message saying that it doesn't exist).
The other reason is that the category structure of this wiki is very weak compared to a lot of other wikis I've worked on. The usual methodology for categories is to form them into branching structures, so that (for example) "Category:Teenage Mutant Ninja Turtles episodes (1987 TV series)" is a sub-category of both "Category:Teenage Mutant Ninja Turtles (1987 TV series)" and "Category:Episodes". Pages would go into the more specific category, and would not therefore need to go into the more general categories.
Following this structure also then helps identify other issues, such as multiple categories with the same purpose and different spelling, much more easily.
I started quite slow because I wanted to see what other people thought about it. So what do you think? Do you think it's necessary for every episode page to be included in "Category:Episodes", or is that just how things have been done and nobody has tried to change it before?
Your assumptions are incorrect. I would have replied regardless, had I known you did.
I don't know what other Wikis you edit, but I don't know of any Wiki that takes kindly to strangers just completely coming in and making revamps without discussion first. There's a difference between being bold and being obstinate.
And yes a "Category:Episodes" is valid, just as we have a "Category:Characters". This is why I reverted as many of your removals as I could find, because we do indeed want that category.
The fact that you've re-removed them after I've reverted your edits that I've explicitly said were valid is a breach of common courtesy and sense. So is your assumption that "silence equals consent".
I'm pretty steamed about this turn of events and to be perfectly honest, you're lucky I'm not blocking you. Consider this a warning.