Consider these statements:
Don't worry about Matt. I will bring he and John home after the party.
Don't worry about Matt. I will bring him and John home after the party.
Is one preferred yet both correct? Is only one correct and the other wrong?
Consider these statements:
Don't worry about Matt. I will bring he and John home after the party.
Don't worry about Matt. I will bring him and John home after the party.
Is one preferred yet both correct? Is only one correct and the other wrong?
"He and John" in this context is an example of hypercorrection.
English-speaking children are often confused about pronouns and will say things like "Me and John went home." (using an object pronoun in place of a subject pronoun when combined with another noun or pronoun, in particular.) They will then learn that the correct thing to say is "John and I went home." Sometimes people (children or adults) will remember this rule and incorrectly extend it to all cases of (noun/pronoun 1) and (noun/pronoun 2), even when this noun phrase is the object of a verb. So in a nutshell, "he and John" is incorrect in your example because this noun phrase is the object of bring. "him and John" or "John and him" is correct (generally nouns are listed before pronouns in these constructions, so "John and him" is preferable, but this is more a matter of style than grammar).
The correct usage is
Don't worry about Matt. I will bring him and John home after the party.
To help figure this out, I dropped John from the statement to consider "him" and "he" alone. For example,
I will bring him home after the party.
To me, this sounded better. Those posting comments to my question confirmed that this was right and the other wrong.
The subject of the verb "bring" is "I". The object is "him and John". Since the pronoun appears as an object, the objective form is appropriate, which is "him". Your friend thinking that "he" is preferred may be an example of an overcorrection. It may be that your friend has incorrectly used the objective pronoun in cases where the subjective pronoun is called for, been told that is wrong, and incorrectly thought this means that "he" is in general more correct than "him", rather it being more correct *in certain situations".