You actually brought up a very good point.

I would really love to learn how a language evolved into its present day form, how it is influenced by the way the speakers thought/think. Kind of like etymology, except for the language itself, not the individual words.

"Me and my friend went to the mall." Remove the "and my friend" part. Would you say "Me went to the mall?" No, that's why you say, "My friend and I went to the mall." Because "I went to the mall" is proper English.

Me = object pronoun.

He gave the ball to me.

I = subject pronoun

I went to the airport.

You would never say "He gave the ball to I" or "Me went to the airport", because I and Me play different grammatical roles.

When you say "my friend and I", it is a compound subject, but the subject of the sentence nonetheless, thus you use "I"

"I and my friend" is still grammatically correct, but cumbersome to say and almost never used.

Cool. Sometimes I think about how much a native English speaking person could teach themselves by teaching it to foreigners. You would have to analyse everything, and develop an explanation as to why such a concept exists, other than "because thats just how it is."