How is Daisy Buchanan a tragic character?
What's tragic about Daisy is that she's capable of love and affection, but chooses to remain stuck in a marriage with a man who clearly doesn't respect her. It's not so much that Daisy would necessarily be better off with Gatsby than with Tom; it's just that she deserves a whole better than her serial cheat of a husband. But because of her innate superficiality and her elite social upbringing, she's learned to value blood and belonging over true love and happiness.
Daisy's main problem is that she's unwilling to step outside her comfort zone; to venture out beyond the confines of her gilded cage of inherited wealth and social respectability. She's presented in some respects as a kind of flapper, a young, free-spirited woman of the 1920s; the epitome of the Jazz Age. But in actual fact, Daisy's pretty conventional. She has the potential to break free from her societal constraints as so many other young women of the time did. But unable to make that final leap of faith, she remains destined to be stuck in her present shallow life of luxurious boredom, deprived of the love that she could've had if only she'd had a little more courage and imagination.
Daisy is tragic because she was raised in a society that made her strive for ideals that would not necessarily make her happy. She grew up believing that old money was somehow better than new money, and that it was especially better than no money at all. This clouded her vision and added to the greed and carelessness that ultimately makes her a tragic character. If she was not so interested in money and the lifestyle it buys, she might have been willing to wait for Gatsby, and may have ended up a much happier person.