Answer
If the player makes the support base a larger area by placing the hand on the ground, it is more difficult to knock the player's center of gravity outside of the support base.
A two-legged animal has a support base with a smaller area so a two-legged animal is less stable. Therefore, a two-legged animal would need a more complex neurological system to maintain balance.
Work Step by Step
To push over a defensive player, the player's center of gravity must be outside of the area of the support base. Then the torque from gravity will help to rotate the player away from the support base and the player could fall to the ground. If the player makes the support base a larger area by placing the hand on the ground, it is more difficult to knock the player's center of gravity outside of the support base.
A four-legged animal is quite stable as the support base has a larger area. However a two-legged animal has a support base with a smaller area so a two-legged animal is less stable. Therefore, a two-legged animal would need a more complex neurological system to maintain balance.