Mollie and the cat are different from the other animals on the farm because they do not contribute.
Unlike the other animals on the farm, Mollie and the cat are described from the beginning as being moochers. Mollie cares only about herself. She wants the humans to take care of her, and as long as she has her ribbons and sugar cubes she is happy. She does not want to work. The cat also makes sure that he does not show up when work needs to be done.
At Old Major’s meeting, the cat shows up last, tucks herself into the warmest place, and does not listen to a word he says. When they vote about whether or not rats are comrades, the cat votes on both sides. After the rebellion, the behavior of the cat is described as “peculiar.” She always disappeared as soon as the work started.
She would vanish for hours on end, and then reappear at meal-times, or in the evening after work was over, as though nothing had happened. But she always made such excellent excuses, and purred so affectionately, that it was impossible not to believe in her good intentions. (Ch. 3)
The cat is in it for herself, such as joining the Re-education Committee to try to get the sparrows to come closer. The other animals look the other way because the cat is cute and cuddly and generally very convincing.
Mollie is as useless as the cat, but she is more vocal about it. She asks if there will be sugar after the rebellion, and does not want to give up her ribbons when the animals decide they are clothing. Mollie is described as “foolish” and stupid. While Boxer, the other horse, vows to work harder and does more than his fair share, the same cannot be said of Mollie.
Nobody shirked | or almost nobody. Mollie, it was true, was not good at getting up in the mornings, and had a way of leaving work early on the ground that there was a stone in her hoof. (Ch. 3)
Mollie is one of the first animals to abandon the farm, disappearing and returning to man’s world so she can be stroked by humans, taken care of, and have her sugar cubes. She had an easy life, and prefers that life. She wants to be a pet.
These animals demonstrate that equality does not benefit everyone. Some animals shirked responsibility on the farm when they were pets while the humans took care of them and the other animals worked. They wanted to remain taken care of, and did not want to share the work. In Orwell's allegory of the Russian Revolution, this is exactly how the wealthy upper classes felt. They did not want to share the wealth. They were happy being on top.
Mollie and the cats always seemed to disappear whenever something important was happening so that they didn't have to be apart of all the madness. Mollie is different because she is not all wrapped up in the "wanting to overtake humans' positions in all areas of life" situation. She wants to be a horse. She doesn't mind being taken care of other people and doesn't have any huge want or need to take care of herself. I believe that the cats would be similar, although they do not play as big of a role in Animal Farm as Mollie does.