In the Grimm's tale of "Brother and Sister", the eponymous siblings leave an abusive stepmother and set off on their own. The brother becomes thirsty and wants to drink, but their stepmother, a witch (naturally), had put a spell on every brook in the forest. Sister warns brother that if he drinks of the brook, he would turn into a tiger. The brother listened to his sister, but his thirst increased. He wants to drink from another brook, but that would turn him into a wolf. By the third brook, he would turn into a fawn, but he could no longer help himself, and he drank. Sister promised she would never leave her brother, and they made a home in the forest.
One day, Brother/fawn begged to go watch a hunting party. He teased the King and his hunters, always eluding them, and returning home to his sister each night. On the second day of the hunt, the fawn was slightly wounded, and a hunter saw the fawn knock and say, "Little sister, let me in." This information he related to the King.
The fawn still begged to go to the hunt the third day, though his sister was very afraid to let a wounded fawn out among hunters, but he insisted. The King gave orders that the fawn should be followed, but not hurt. The King followed the fawn and, when he saw Sister, asked her to be his wife. She agreed, on the condition that the fawn always stay with them.
The stepmother, meanwhile, heard of her step children's fortunes and was jealous. She determined to put her own daughter in the new Queen's place. The stepmother made a great fire in the bath-room and suffocated the Queen, and placed her daughter in the Queen's bed-just after the Queen had given birth. Claiming the Queen was ill, the stepmother would not let the King look in the bed where she lay. Each night, the Queen's ghost came into the room, fed her baby, stroked the fawn, and left. One night, she told the fawn, "My child my fawn twice more I come to see, Twice more I come and then the end must be." The nurse told the King of these strange events, and he watched the next night, as the Queen proclaimed she would only come back once more. The King, recognizing her as his wife, restored her to life. The evil daughter was sent into the woods and devoured by wolves, and the witch burned. As soon as the witch was burned, the fawn resumed his human shape. "Then the sister and brother lived happily together until the end."
I was reminded of this tale when I mention Madame de Beaumont's Prince Cherry the other day. Prince Cherry features a prince who is turned into an animal because of his cruelty-first he is a combination of dangerous and feared animals, then with acts of kindness he gradually assumes less threatening forms-a dog, then a bird, and finally back to a man. "Brother and Sister" shows similar results of what would have happened if Brother had given into temptation right away- first a tiger, then a wolf, and then a fawn. Though Brother was punished for succumbing to temptation, he is given a lighter punishment because he waited longer.
Tales of human/animal transformations certainly have many different meanings, but in these tales I think the point made is highlighting the difference between humans and animals. And certainly, there are multiple differences there too, but one of them being that humans have the capability of making moral choices, whereas animals are driven purely by instincts. Humans also follow instincts, but we can be motivated to deny our immediate gratification either by knowledge of beneficial long-term results (studying hard now to get a good job later, saving now to retire later, denying that second dessert helping for the sake of your health, etc.) or to benefit another. Humans also show differing levels of discipline, like the different animal progressions in the above mentioned tales. This is why I get annoyed when people equate Beauty and the Beast with bestiality. If the Beast has the form of an animal, but the capability to love and care for Beauty, therefore proving he has disciplined himself not to act only to satisfy his immediate desires like an animal, he is a man in disguise, and not an animal.