Do giving and receiving equal exchanging?

Recently I was chatting with a friend.  About what, I don't remember.

At one point in the conversation, though, I changed whatever the subject was, and asked, "About gifts," referring to Christmas gifts, since Christmas Day is less than a week away, "did we decide not to exchange any?" 

To me the question made sense when I asked it.  I have a few relationships in which over the past few years we have decided not to exchange gifts.  I thought maybe this may have been one of them, but I wasn't sure.  I just wanted to clarify the expectations.

My friend, though, seemed taken aback by the question.  "Well ...," she began, and I don't remember exactly how she phrased it, but it was instantly clear she had prepared a gift for me and for Japhia.  Separate gifts, in fact.  Simple, not expensive, thought-out, and hand-made.  She explained that whatever I did or didn't do was fine, but she just likes to give gifts. 

I wonder when I started to think of gifts as something we exchange.  Instead of simply give.

It's not like I haven't received gifts from people to whom I did not give one.  

Nor that I haven't also over my life simply and freely given something to others just for the pleasure of giving.  With the question of receiving something in return being irrelevant.

So I wonder about this concept of "gift exchange."  

And I marvel at the ability and willingness of the human heart just to give.