A commenter has said that anything that, from a Christian perspective, all we experience is ultimately only "borrowed" from God - from this perspective, our emotions have no more substance than those of dolls at a children's tea party. A non-theistic perspective at least allows us to have our own emotions.
I think this underplays the Christian perspective, and it also overplays the non-Christian one. From a non-theistic perspective, our emotions, whilst they may not be derivative, have no significance. The fact that (for example) my wife matters so much to me, or that I care so much about people dying of AIDS in the developing world, amounts to a cosmic zero, because my consciousness is simply a by-product of my genes' struggle for survival - no, even that implies too much significance - the fact that over the course of time, some sequences of DNA are chemically more likely to reproduce than others. And ultimately the whole universe is a zero - a quantum fluctuation that happens to be here, but might just as easily not have been.
But people don't operate on that basis. They care for themselves - they make sure that they are sheltered, fed and even pampered, as far as they are able to. They make moral decisions - not believing that they are actually cosmic zeroes, but as though it actually matters. As before, I know that you can talk in terms of the evolutionary advantages of altruism and love, and so on, but the problem is that every term needs to be replaced with zeroes. Altruism is zero. Love is zero. Evolution is zero. Everything is zero - because if not long before, at the time of the heat death of the universe, there will be nothing left. No matter what other factors you use, zero is one of them - so the product is always zero. I am not satisfied with the atheistic worldview because I don't believe that people genuinely operate as though it is true.
What about from a Christian perspective, then? Can we get past the idea of derivative emotions - that they have no significance because they are only what God has put there?
In the past, I have used the analogy of a computer program and a programmer to think about the relationship between us as created and a god as creator. Supposing a program is written to evaluate some data, in some circumstances, and make an assessment of the characteristics of the writer that have been specified. Supposing that it says: "J. Smith, who wrote this program, is cool." From the program's point of view, this reflects a genuine interpretation of data, a conclusion that it freely came to. From the perspective of the programmer, he may be able to say: "Well, the program was always going to come to that conclusion."
As a Christian, I believe that God has "programmed" us, and that he does know how we are going to respond, and what the outcome of all our decisions is - I have a strong view of the sovereignty of God. But whilst I have that view, I don't know what God's purposes are. I don't know what God intends to happen. And as far as I am concerned, the decisions I make are freely made. Our response may be deterministic, as far as God is concerned, but God's hand is so imperceptible that from my perspective it is indistinguishable from me being free. I am far freer in what I express than any computer program, let alone any doll at a child's tea party.
You only have to look at the Bible to see that this is a fair reflection of the nature of things. Would Adam and Eve really have eaten from the tree of the knowledge of good and evil if they had known what would happen? Would Judas really have betrayed Jesus if he had known what would happen next? Would you have? And yet, Jesus had pretty much told him that he was going to be betrayed. The contrast between "the purposes of evil men" and "the foreknowledge of God" is brought out strongly in Peter's sermons in Acts.
I think this is why the narrative idea of nemesis/destiny/fate is so strong, in all sorts of cultures (Shakespeare, Tolkein, Homer, ... er, Rowling). People know that this is how the world is - that regardless of the freedom that they perceive, there are "forces at work" which bring about particular ends. From a Christian perspective, those forces are embodied in the sovereignty of God.
The idea of the Christian God, and human nature is stronger than that. We are created - but we are created to respond as we choose. Imagine a better computer program, now - one that can evaluate data about everybody in the world, and come to a conclusion about who its "favourite" person is. Supposing this program still concluded that the writer was a cool person: wouldn't the programmer be more satisfied with its response, even though (in principle) it is possible to establish that it was always going to say that? How good would a computer program have to be before the programmer would "take delight" in its responses?
A program has an "About..." box, which includes copyright and licence details. Supposing somebody hacks into the program, and replaces the contents of the About box with his own details. Would not the original programmer be rightfully angry with the hacker?