Cycles exist because they are excruciating to break. It takes an astronomical amount of pain and courage to disrupt a familiar pattern. Sometimes it seems easier to just keep running in the same familiar circles, rather than facing the fear of jumping and possibly not landing on your feet.

This quote takes place in Chapter Thirty-Five, after Emerson is born and Lily decides that she needs to divorce Ryle. Here, she acknowledges how resistant cycles are to change. Because it is so painful to change deeply engrained habits, people often choose to stay with what’s familiar, rather than going through the painful process of moving into the unknown. Lily is frightened to leave Ryle and frightened to move away from the familiar pattern of abuse and reconciliation that framed not just her relationship with him but also her parents’ marriage. However, she can no longer lie to herself. She can no longer convince herself that it’s possible to stay in the relationship and be happy, change Ryle, or heal him from his rage and pain. After much soul-searching, she knows it’s the only way for her and her daughter to find a new way forward. By breaking the cycle, she even brings healing to her mother, helping all three generations find a way to be free.

My mother went through it. 
I went through it. 
I’ll be damned if I allow my daughter to go through it. 
I kiss her on the forehead and make her a promise. "It stops here. With me and you. It ends with us."

This quote takes place in Chapter Thirty-Five, as Lily strengthens her resolve to protect her daughter from the cycle of abuse she grew up with. Lily finally decides that she can’t stay with Ryle. What ultimately pushes her over the edge is seeing her newborn daughter. Lily spends her teenage years wishing that she could save her mother or that her mother would save herself. Lily couldn’t change that situation, which parallels the way that, once Ryle starts hitting her, she feels stuck in the relationship, unable to free herself, trapped in a nightmare. For a time, she feels as though she’s not strong enough to leave and her love for Ryle is stronger than her love for herself. But, seeing her daughter, she knows she has to do what her mother couldn’t because it's the only way to stop the cycle of abuse. 

He presses a gentle kiss there and it feels just like the first time he kissed me there all those years ago. He brings his mouth to my ear, and in a whisper, he says, "You can stop swimming now, Lily. We finally reached the shore."

This moment between Ryle and Lily takes place in the Epilogue, when the couple finally returns to each other, ready to start a new life. Breaking up with Ryle is just one part of ending the cycle of abuse for Lily. She also must make a new decision in her next partner she has, to ensure she doesn’t replicate the pattern with a new person. Here, Atlas gives her a “gentle” kiss, evoking their first kiss as teenagers, in which Atlas treated her like she was made of eggshells. Atlas knows how strong Lily is, but he also begins this next phase of their relationship with tenderness, which emphasizes how different he is from Ryle. Atlas has always shown Lily respect, gentleness, patience, and kindness. In getting together with Atlas, Lily is able to stop swimming away from abuse and to stop feeling like she’s drowning in grief and violence. By reaching the shore, the couple has found a solid place to build their life together away from the pain and struggle of their youths and to start a new chapter, together.