You’re skirting the issue and you know it. Either 1) God give you your faith or 2) you generate it from hearing God’s word. You can pick door #1 or door #2 but there isn’t a door #3.
My understanding of the reformed view is that it is not "either or" but "both and." That is, it is YOUR faith. It is not God's faith, but truly yours, exercised by a moral, choosing being. Nevertheless, that faith is the natural and irresistable choice of a regenerate nature. Ask a child whether he "chooses" spinach or ice cream, and he will choose ice cream every time. No one forces him to do so, he simply chooses (with a hat tip to Jonathan Edwards) according to what seems best to him, or most desireable to him. I personally believe (and there is some degree of biblical evidence for this) that faith is an act of the will. However, the biblical picture is that our will is in bondage (again, hat tip to Luther) to our sinful nature, and only chooses as our sinful minds and natures dictate. Therefore, when God makes us alive by a sovereign act of the regenerating Holy Spirit, suddenly we see the beauty and glory of Christ (we were blind before), the danger of our own unbelief (at which we mocked before) and the great love of Christ in dying for ME! The natural and most reasonable thing in the world for a man made alive is to fling himself into the promises of Christ...., and he does.
So is faith a gift? Sure! Not in the sense that it is not MY faith. I exercise faith. God does not do it FOR me. However, because it ONLY comes from a regenerate spirit, it can truly be said to be a GIFT.
And what is wrong with door #3 --- Romans 10:17: "Faith comes by hearing, and hearing by the word of God"
Show me from the scriptures where one is born again before he hears the word of God???