There is an important piece of grammar that I think basically everyone I know gets wrong. English majors get it wrong, professors get it wrong, TV shows get it wrong, people on the news get it wrong - like I said, most people I know personally or see in the public eye get it wrong.
I admit - especially for an English major - I have a high tolerance for grammatical errors. I don't cringe every time someone messes up. I notice it, but I let it go. I'm chill.
This error gets to me every time, though. Not because it's an error, either, but because it's a conscious error. It's people deliberately making this mistake because they think it's correct. And that bothers me.
Do you remember, growing up, when you used to say things like, "Emily and me are going out to play?"
I'm sure some adult (parent? teacher?) would gently correct you with, "Emily and I."
So you learn, "Emily and I are going out to play."
And forever after, you are conscious of not making the same error twice. But that eventually translates into...
"Would you like to come play with Emily and I?"
This should be right, shouldn't it? After all, you remember going over and over, "Emily and I, Emily and I, get this right, it's Emily and I."
You see, when I was taking Latin, I learned about two grammatical cases that most people would probably translate as "subject" and "object." They were called "nominative" and "accusative" and they have different endings that I had to memorize, just like in English, really, but we don't think of it that way in English. Now, the nominative word or subject of the sentence is not what the sentence is about, but who or what is doing the action of the sentence. So in the sentence, "Emily and I are going out to play," Emily and I are doing the action. We are the subjects of the sentence. "I" is the nominative version of first person singular (I, me).
However, in the sentence, "Would you like to come play with Emily and me?" the person doing the action is "you." You are coming to play, even though it's a question. If you turn it into a statement, it would be, "You like to come play with Emily and me." Not "Emily and I," but "Emily and me." "Me" is the accusative version of first person singular. "Emily and me" are the objects because the action is being done to them, or with them, or for them, etc.
You might be thinking, "okay, but in normal speech, no one is thinking that carefully about how they structure their sentences." True - but, first of all, you should! The more you try to be grammatically correct, the more naturally it'll come to you, and then you won't have to think about it anymore. But I know, if you don't care, and if no one else seems to care (except crazy grammar freaks), then what's the big deal?
The big deal here is that people constantly make this mistake because they are trying to be grammatically correct and doing it wrong.
Here's an easy way to remember the correct word to use for "I" and "me." Change it to third person.
Naturally, you'd know to say, "She goes out to play" but "I go out to play with her." You wouldn't say, "I go out to play with she," would you?
She, he, I. Him, her, me. That's how it goes.
"Emily and me" can be correct and is correct when used properly.