By "wrapper" I assume you mean tag? Anyway, if that's literally what you have in your document, then I'm not surprised that Firebug might not react the way you expected. You shouldn't use typographer's quotation marks ("curly quotes") in HTML markup. Try replacing them with straight quotes and see what happens.
Other than that, if you have the HTML tab/panel showing on the left, and the Style panel showing on the right, then selecting something on the left should show any styles that apply to it on the right. That assumes there are styles defined for it.