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If you came here to complain about how this differs from your view of English grammar: we teach real German and English, not a grammarian's dream of how a language should behave it it were Latin.
Remember that German has a very active case system. That means that Ich auch, mich auch and mir auch are all used, but in different circumstances.
Ich bin Lehrerin. Ich auch.
Er schlägt mich. Mich auch
Mir ist kalt. Mir auch.
What ever case the noun or pronoun represents in the sentence you are saying also applies to you will be represented with the correct pronoun here.