I agree, I think "love" is an inadequate word used to describe a broad range of emotions and actions. Defining "love" in English is nearly impossible, since you have to set the stage so completely to even ask the question. I mean, we "love" these shoes, "love" our mate, "love" our children, "love" asparagus, "love" our neighbor... etc. All a completely different meaning.
When I first left the JWs I had a terrible time with the "agape" concept of love, but finally came to the conclusion that, for myself, this kind of love shows itself when you feel care and compassion for individuals you have never met. It shows in tears for strangers in tragedy, joy for strangers in abundance. This is a far cry from the type of "love" I feel for family.
It seems unfortunate that we only have the one word, and must come up with an entire story to explain what is meant.