I'm not an English scholar, but I do notice a few things every so often. When I was an elementary school, we, kids, often made the mistake of saying things like John and me are going outside only to be promptly corrected by the teacher who would say, John and I are going outside. But typically, that's all our teachers would say about the usage of me. The problem is that it seems teachers everywhere made such a point of correcting this that many English speakers no longer know when it is proper to say John and me or improper to say John and I.
For example, I hear many adults saying things like, I'm doing this for my family and I or Between you and I, I think we're scones! These usages are not correct because the pronoun "I" can only refer to the subject of a sentence (nominative case), not the object. The proper usage in these examples would be, I'm doing this for my family and me or Between you and me, I think we're scones!
I think it is best summed up here:
Between you and me is acceptable in standard English; between you and I isn't. This is because between is a preposition, and pronouns that come after prepositions are in the accusative case (here, me), not the nominative case (not I).I wasn't aware of the difference myself for years.
The same applies to a pair of pronouns that is the object of a verb: They've invited you and me to dinner is acceptable, They've invited you and I to dinner isn't.
The reason why expressions like between you and I have become so common is that people are aware that the accustive case is not correct for the subject of a verb ( You and I have been invited is acceptable; You and me have been invited is not), so they make the mistake of thinking it is not correct anywhere, and always use the nominative case.
If you are in any doubt, try leaving out the first pronoun of the pair. That will show you what case the second one should be: between I and they've invited I are clearly ungrammatical.