Question

Why doesn't an animal cell have a cell wall?

Answer 1

The role of a cell wall is to keep the cell rigid and provides protection. Animal cells do not need the cell wall as they have other forms to keep themselves rigid such as the skeletal bones whereas the plants have none of those and thus need the cell wall for rigidity.

Answer 2

It is generally an advantage for plants to stand upright and grow as tall as possible. Plants need sunlight, so growing taller than neighboring plants make it more likely that the plant will survive and successfully reproduce. For animals, height may be an advantage sometimes as well, but most animals have skeletons and musculature. They do not need the rigid network that cell walls provide to stand upright.
Furthermore, most animals can move, and this capability is an enormous advantage when it comes to feeding, finding a mate and escaping from predators.