Check these two links:
That link takes me to my home DuoLingo screen. Is there a short answer to this question?
Because its remaining or staying on the wall. Being on the wall is not an essential aspect of its nature. See the link posted by @dnovinc above.
By the same token, being on the table is not the essential aspect of a plate's nature, yet, usiamo "e" (e.g., l'uovo e nel piatto).
Essere=to be; to exist. Stare=to stay and sometimes to remain. With these verbs, you often have to go beyond the literal translations and think idiomatically since both verbs have numerous usages. Both verbs can be used to express a location. In this translation, I only can infer DL is offering up stare to teach a new verb and its specific use for a permanent location as opposed to using essere for a more temporary location. Perhaps the translation could have provided a hint to the mirror's permanent status by referring to it being large and not an item easily relocated.
The second link above specifically states that location (including for furniture) is generally essere. Is this just one of those you have to memorize?