The reason why cats tuck their paws in:
1. In winter, when cats feel cold, they will tuck their paws in to keep their paw pads from the ground in order to keep warm.
2. If a cat tucks its paws in and yawns or stretches, it means the cat is in a relaxed state. 
3. When a cat is sick, it will curl up and tuck its paws in. The owner needs to observe whether the cat is injured or has a disease.
4. A cat's paws are very sensitive. To prevent its owner from touching its paw pads, a cat will tuck its paws in.
5. When the owner wants to trim the cat's nails, the cat gets scared and tries to protect its paws by tucking them in.