When Gatsby proposes that Daisy leave Tom in The Great Gatsby, he is suggesting that she leave her life behind to begin a new one with him. This is significant due to the profound implications for Daisy's future as well as her past.
Though Daisy did love Gatsby when she met him when they both were young, before Gatbsy went off to the war, she has been with Tom for quite a while by the time she reunites with Gatsby. She has a troubled relationship with Tom, but she also has a history with him. Leaving this history and the well-known confines of her marriage for an unknown future with Jay Gatsby is quite a bit decision.
Essentially, Daisy is choosing between a life she knows and a life she does not.
Also, when Gatsby insists that Daisy say that she never loved Tom, Daisy faces a similar conflict. Gatsby is asking Daisy to say that her life up to this point has had no meaning. He is asking her to erase her past. She cannot do this and refuses.
Ultimately, Daisy cannot turn away from her past, cannot rob herself of significance by robbing her past of meaning, and cannot choose the unknown that Gatsby offers in favor of a familiar, yet damaged marriage to Tom.