Thanks for bringing this up and a warm welcome to our site!
Are there any good reasons for not having this tag?
This sounds like a very reasonable tag idea.
I'm not sure what the best wording is, but negation is certainly a good idea.
A tag can also have multiple names — or, more accurately, tags can be synonymized or merged.
Names can be changed later on.
How may I further push for having this tag added?
By bringing it to meta; this is the perfect approach.
I have now created the tag negation by adding it to a question.
Any user with at least 150 reputation can create new tags by simply typing in the new tag name in the tag selection box.
Informal discussions about tags and all else can be had in our chat room.
You need 20 points to talk in chat.
Now that the tag has been created, a couple of things need to be done to make it useful:
Add it to other questions.
Anyone can look for questions in need of such a tag and add it.
Starting at 1000 points, any user can edit questions (including tags), and users below the threshold can suggest edits for others to review.
Approved suggestions earn a little bit of reputation.
Since editing a post will bump it to the front page, please don't edit all the possible posts at once.
In order to not flood the front page, about three edits of old posts per user per day is reasonable.
Edit the tag wiki.
It's enough to write a short usage guidance in the tag wiki edit page.
It could say, for example: "For questions about negation, such as the usage of the words 'non' and 'ne'."
It should be short and free of formatting.
Anyone is free to edit any tag wiki we have.
It can be done directly by users above 1500 points, and others will have their suggestions reviewed.