One kind of fish, the hagfish, is considered an invertebrate by scientists. Why is this fish an invertebrate whereas all other fish are vertebrates?

4 answers

http://www.seasky.org/deep-sea/atlantic-hagfish.html
The Myxini are unique among living chordates in that they have a partial cranium (skull), but no vertebrae, and so they are not truly vertebrates. The skeleton is composed of cartilage, and lacks bone.
As a note on the question, the classification of Hagfish as invertebrate is under dispute, and far from agreed on. I am surprised your instructor moved you into this area of dispute.
4. One kind of fish, the hagfish, is considered an invertebrate by scientists. Why is this fish an invertebrate whereas all other fish are vertebrates?