So what's wrong with Four Loves?

That's a long answer. A short introduction to the long answer might go like this:

Lewis says the Greeks have four words for love and we have only one. That's sort of but not really true. We have other words such as Friendship to mean something pretty close to (close enough to) philia.

And come at the telescope from the other end and we might say, the Greeks have these four words but none of them and even all four put together don't quite mean what we mean by love. Our word may well be better and it may be—I'd argue that it certainly is the case—that we can get a much better understanding of what agape means if we begin with the meanings of the modern English word love than we will ever get of love by starting with agape.