The speaker is trying to explain what "the wolf" means, and the answer is that it isn't an animal at all. It's an idea. Nobody in the poem is literally a wolf; instead, the wolf is a person who is pretending, someone who acts like they're one thing while being another. The repeated line "The wolf is a concept" works like a definition the speaker keeps returning to, as if they need to say it twice to make it stick.
The feeling underneath seems to be hurt and distrust. The speaker talks about someone who seems different from you "in some way, shape or form," but then says "they're not," and the plain, blunt phrasing makes the accusation land. Words like "lying," "pretending" and "not being true" come in short, stacked lines, almost like a list of charges. The mood is quiet but bitter, the tone of someone who has been fooled by an act and is now seeing through it, perhaps with some lingering anger at having been tricked.