If the point is to be able to identify the type of dependent clause (sometimes called subordinate clause) for a grammar test, and not to use that information for any further work, then I agree with your son. Knowing the names of some constructions seems a waste of time.
However, as he becomes a more mature writer and analyzes his writing in order to improve it, knowing how to identify certain constructions can be useful.
For example, suppose he writes a paragraph and has the impression that there is a sameness to the sentences, but he can’t figure out why. If he analyzes the paragraph for sentence construction, he might see immediately what the problem is. Take the following paragraph, for example.
1 My friend, Bob, invited me over for pizza after we finished soccer practice. 2 Of course, I said yes, since I was famished. 3 We ordered a mushroom pizza because Bob is a vegetarian. 4 The delivery man came late since he encountered a car accident down the road. 5 We tipped him extra even though neither Bob nor I have much money. 6 Man, that pizza tasted good!
Now let’s analyze it.
Sentence 1—independent clause, adverbial dependent clause
Sentence 2—independent clause, adverbial dependent clause
Sentence 3—independent clause, adverbial dependent clause
Sentence 4—independent clause, adverbial dependent clause
Sentence 5—independent clause, adverbial dependent clause
Sentence 6—independent clause
Five of the six sentences above follow the same construction: an independent clause followed by a dependent adverbial clause. The dependent clauses begin with four different words (after, since, because, since, even though), but they all come at the same place in the complex sentence.
Knowing this, the writer could easily add variety and reader interest to his sentences. He could put one of the dependent clauses at the beginning of the sentence. He could turn one of the complex sentences into a complicated simple sentence. He could turn one of the complex sentences into a phrase. He could combine two of the sentences into an extended sentence. He could add a direct quote.
In every field of study, we need specific vocabulary words to identify what we are thinking about. Grammar is no different. But knowing the words is useless unless we use the words for some purpose that makes sense to the user.
Perhaps you could talk to your son’s English teacher and tell her/him about the problem your son is encountering. Perhaps the teacher could connect the skill of identifying types of dependent clauses to further study—even if that study will not happen in sixth grade. Connecting what we learn to the real world (in this case, the world of writing) is important to motivate students to learn. I remember being in trigonometry class in high school, and asking the teacher why I needed to know sine, cosine and tangent. She couldn’t give me an answer. My desire to learn that math was low.