Panel 1: We find Liz staring at Farley and smiling ruefully while at the same time telling herself that he likes her no matter what. This tells us that we're in for a bit of Old Dog Trey stuff about how the world would be a better place if people were more like dogs.
Panel 2: She makes a sweeping. Hallmark card-worthy generalization about how dogs don't care who you are or what you look like, they love you anyway.
This means that Farley has just been elected Living Emotional Crutch by a girl obsessed with the idea that she's about to be a pariah no one should love because she's the creation of a middle-aged drone who fears having to wear eyeglasses because they're a sign of her oncoming death due to ooooooooooooooold age.
Panel 3: We further this by having her state that the purpose of a dog is to make everyone happy. This seems odd to me because a cursory reading of the strip tells us that the purpose of this dog is to be abused and neglected by imbeciles so that a nutjob can simper about people not caring about people with world diseases.
Panel 4: Since she's
Summary: The problem with pandering like this really isn't going to help Liz in the long run. What would help is admitting that the Mikes of the world are anomalies who should be spurned like rabid dogs even if the horrible things they say match up with the self-loathing in her heart. Ah, well. You can't fix self-harming.