Part of what makes The Great Gatsbyso compelling is that Fitzgerald creates a world where secret is layered upon secrets. There is no real human connection to anyone as secrets become the filler for the space between individuals. It is in this real where one can find many secrets. Had these secrets not been there, a more real and substantive human connection between individuals would have been present.
One such secret that ends up creating a conflict is that Tom's marital indiscretions. Tom cheats on Daisy at many points in their marriage. The narrative places a heavy emphasis on Tom's relationship with Myrtle, something that he never reveals to Daisy. The damage in confessing such a reality might not have been much. Daisy does not act on the fact that there is no real love between them. Perhaps, socially, Daisy might have had a reason to leave Tom. This could be seen as the damage had the truth been revealed. Another secret is that Tom kills Myrtle. This secret is concealed, again by Tom. If Tom tells the truth, then he would be liable both legally and morally for Myrtle's death and George would have had a direct target for his anger, as opposed to the misguided anger he felt towards Gatsby. Similar to keeping his indiscretions a secret, Tom gains much from this concealment. Finally, I think that Daisy keeps the secret to herself tht she does love Gatsby. About as much as Daisy can love, she does have feelings of love or at the very least affection towards Gatsby. Even if one argues that Daisy is incapable of love, it could at least be suggested that Daisy has fallen out of love with Tom. This is a secret that she does not act upon, and something that she does not reveal. If she were to disclose it, she would have to live with the consequences of her emotions and accept them as a part of reality, something that she does not wish to do in choosing Tom over Gatsby. Characters in Fitzgerald's story keep their secrets because these secrets have helped to construct the world and their place in it. The damage done by revealing such a condition forces them to configure new worlds, ones with more reality in it. Fitzgerald makes it clear that this is not seen as a viable option.