EDIT: it seems that a further explanation on the purpose of tags is warranted. They have a very specific purpose at Stack Exchange.
Tags are meant to be "subjects" or "topics" to help people find posts that are about them but don't necessarily contain the words.
For example, posts about the language C# on Stack Overflow are tagged C# and do not contain this keyword.
Tags are used so people can filter the site's question lists on a combination of them, so for example people interested in biology can see all biology questions on this stack exchange by going to biology. Most of these questions won't have the word "biology" in them, because it's their topic. Only 7 questions tagged biology also contain that word.
The "correct" tag is whatever topic people use to filter questions by. Adding entomology is fine in this sense -- it's likely that people interested in insects are also interested in spiders.
If people are interested only in spiders, then searching by the tag spiders was always the wrong choice. Tags are not keywords. The correct, much superior way of looking for spiders questions is using search. Only six questions where tagged spiders, but 18 posts have the keyword spiders in them.
Adding a separate arachnology tag for arachnids (and not only for spiders) is fine, but frankly, as long as nobody is looking for arachnology questions, it is useless. Actaully it is worse than that. What will happen is that people tag some question spiders, some other questions arachnology (which I doubt since no one tagged questions "arachnids" in the first place), and most will simply use "insects" which is then remapped to "entomology".
I don't think we want that.
Keep in mind that adding obscure tags that almost no one uses is noise, which is why creating tags is a privilege. The community is expected to clean up useless tags via retagging (zero usage tags are removed nightly). Moderators can merge when the do not want to make the questions appear on the homepage.
Tagging is hard.
We shouldn't have a tag for 6 questions only. This rules out both spiders and arachnology, especially since while insects and spiders are different, it's quite possible that questions tagging one should also tag the other.
You are correct that techincally entomology is imprecise. It is, however, the historical term. However the correct science which includes both arachnids and insects is arthropodology, which has the downside of including also crustaceans and not being very used (this could be fixed by adding appropriate aliases)
We decided long ago that using the name of the science for tags is the convention we want, and this seems non-negotiable at this point.
Arthropodology would need us to retag all questions about crustaceans to that, do we want this? Any better names?