"Mi amigos" is a mistake because "mi" is singular and "amigos" is plural. The correct is mi amigo, mi amiga, mis amigos, mis amigas.

You must think of "mi" as a possessive adjective and follow the rule of Spanish that says that adjectives must agree with the nouns they qualify in number. If the noun is plural, the adjective has an -s, too; if the noun is singular, then the adjective has no -s and you say "mi". It is true that "mi" and "mis" do not quite behave as typical adjectives, since typical adjectives agree with their nouns also in gender, whereas "mi/mis" is invariable as to gender. Observe, though, that gender agreement is obligatory with "mi/mis" when they are postnominal and stressed: "un amigo mío/*mía", "una amiga mía/*mío", "unas amigas mías/*míos" etc. And observe as well that many adjectives are invariable in gender anyway (e.g., "grande", "útil", "feliz", etc.). Your difficulty is understandable, nevertheless, because the plural marker is redundant: Why should the word/phrase that expresses the possessor agree with the word/phrase that expresses the thing possessed after all? English is less redundant in this respect than Spanish, French, Italian or German, but lots of things are 'redundant' (and yet very useful!) in Spanish and in all languages. Redundancy is often functional: it is there to make processing easier :-).