The way I understood it is thus:
Beth has just realized that Dawn's power lies completely in making others subservient to her, and Dawn knows it. Dawn needs a ward who will listen to her and obey her. Noah filled that part prior to Beth's arrival. When Noah escapes, Dawn now needs to bind Beth to her, so she starts being nicer to her, covering up for her involvement in Gorman's death, and helping her get drugs for Carol ... etc. At the time Beth interpreted these actions as Dawn genuinely wanting to be a better person.
But when the hostage exchange happens, and Dawn demands Noah's return Beth suddenly understands. Dawn needs a ward. Now that Beth was slipping out of her hand, she needed to have Noah back. "I knew you would be back" was Dawn projecting her desperation for someone to need her as a false hope. With Dawn's true motivations exposed, Beth wanted to end the cycle of abuse that resulted from Dawn's broken psyche and decided to kill her.
Note how the atmosphere in the hospital immediately changes when Dawn is dead, the female officer says, She (Dawn) was the problem, and the hospital residents offer shelter and alliance to Rick's group with no strings attached.
Also, earlier in the episode, or the previous one, Noah says the exact same phrase, "I get it now", when referring to Dawn as she seeks weak people to serve under her. Later on, Dawn tells Beth "I thought you were weak, but you're not", after she learns of Beth's escape attempt.
She gladly gives up Beth as an exchange because she doesn't want someone stronger than her. Dawn feels threatened by Beth's strength.
When Beth says "I get it now", and attacks it's probably because she knows Noah will be badly mistreated again and is protecting him.