I hear people saying, "He said it to my wife and I" when they would never say, "He said it to I." Why are people so inconsistent?
There is a discussion of this issue on page 9 of the Cambridge Grammar of the English Language (CGEL), a descriptive grammar. Here is a lengthy extract in which the authors, Pullum and Huddlestone, make the case that expressions such as 'they invited my partner and I to lunch' are grammatical.
Another kind of illegitimate argument is based on analogy between one area of grammar and another. Consider yet another construction where there is variation between nominative and accusative forms of pronouns:
 a. They invited me to lunch.
 b.% They invited my partner and I to lunch.
The ‘%’ symbol is again used to mark the B example as typically used by some speakers of Standard English but not others, though this time it is not a matter of regional variation. The status of the construction in B differs from that of It’s me, which is undisputedly normal in informal use, and from that of !Me and Kim saw her leave, which is unquestionably non-standard.
What is different is that examples like B are regularly used by a significant proportion of speakers of Standard English, and not generally thought by ordinary speakers to be non-standard; they pass unnoticed in broadcast speech all the time.
Prescriptivists, however, condemn the use illustrated by 3b, insisting that the ‘correct’ form is They invited my partner and me to lunch.
And here again they seek to justify their claim that 3b is ungrammatical by an implicit analogy, this time with other situations found in English, such as the example seen in A. In A the pronoun functions by itself as direct object of the verb and invariably appears in accusative case. What is different in B is that the direct object of the verb has the form of a coordination, not a single pronoun. Prescriptivists commonly take it for granted that this difference is irrelevant to case assignment. They argue that because we have an accusative in A we should also have an accusative in B, so the nominative I is ungrammatical.
But why should we simply assume that the grammatical rules for case assignment cannot differentiate between a coordinated and a non-coordinated pronoun? As it happens, there is another place in English grammar where the rules are sensitive to this distinction – for virtually all speakers, not just some of them:
4 a. I don’t know if you’re eligible.
4 b. I don’t know if she and you’re eligible.
The sequence you are can be reduced to you’re in A, where you is subject, but not in B, where the subject has the form of a coordination of pronouns.
This shows us not only that a rule of English could apply differently to pronouns and coordinated pronouns, but that one rule actually does. If that is so, then a rule could likewise distinguish between 3a and 3b. The argument from analogy is illegitimate. Whether 3b is treated as correct Standard English or not (a matter that we take up in Ch. 5, §16.2.2), it cannot be successfully argued to be incorrect simply by virtue of the analogy with 3a.
I am not totally convinced by this argument, and I would be interested in reading evidence that "... examples like B are regularly used by a significant proportion of speakers of Standard English, and not generally thought by ordinary speakers to be non-standard; they pass unnoticed in broadcast speech all the time." For me, such expressions are often instances of hypercorrection based on what Pullum himself on Language Log calls "nervous cluelessness" about grammar, based on half-remembered half-truths from their school days - often imparted by teachers using Strunk and White as their bible.
However, later in the CGEL (p465) Pullum explicitly rules out hypercorrection as the source of such expressions:
Because these coordinate nominatives are perceived to be associated with avoidance of stigmatised accusatives in subject coordinations they are often described as hypercorrections. This is to imply that they are ‘incorrect’, not established forms in the standard language. Construction [1 above (It would be an opportunity for you and I to spend some time together.)] with I as final coordinate is, however, so common in speech and used by so broad a range of speakers that it has to be recognised as a variety of Standard English ... .