I don't understand it yet. I'm German, so maybe it is just a problem with translating the words. "Mig" in German would be "mir" or "mich". But: "Det er mig" - "That (or it) is me" in German would be "Das bin ich" or "Ich bin es". So "mig" would be "ich" ("jeg"). Is it just the sentence that doesn't work with German or is it my weird thinking? I don't understand the objective thing here.??
The fact is that the unit is called "object pronoun" but most sentences have just subject words. I am Italian and I would say "sono io" to translate it is me and never "sono me". In this case "me" is the person who performs the action of being and this in grammar is a subject not an object. I can see it is the same in German and Spanish, Danish and English are a bit confusing on this point.
this is the first sentence I find in this unit and it is a bit confusing in a grammatical way (though it is quite is to use and translate). there is not a real object in this sentence. I am the subject and the object of the sentence at the same time. not a great example, I think.