@millie because Anna is too good for lily. Lily is a person that can't distinguish love from lu** and, in a way, rose is the same. You can see that at some point, lily is forcing Anna with her indecision to do something she didn't want to because of a past trauma. So it's better to be with someone that has the same way of thinking about"love"than with someone that has another. Anna totally deserves somebody that can wait for her until she is completely ready