A legal system can only be effective when the public trusts the system to administer punishment evenhandedly. Corporal punishment is not administered evenhandedly due to societal influences. Therefore, corporal punishment leads to reduced public trust in the legal system.
Due to societal and cultural norms around gender, boys are always on the receiving end of harsher corporal punishments. If a punishment system cannot be administered evenly across all demographics, it should not be used.  If a punishment method is adopted that does not punish all offenders evenly, the public will lose trust in the legal system and the rules-based order is undermined.
Corporal punishment is meted out evenly. A study in the US found that 67% of mothers and 68% of fathers slapped or spanked their children as a punishment and there was no apparent gender difference between boys and girls. 
[P1] A legal system can only be effective when the public trusts the system to administer punishments evenhandedly. [P2] Corporal punishment is not administered evenhandedly. [P3] Therefore, corporal punishment erodes public trust in the legal system. [P4] Therefore, corporal punishment should not be allowed.
Rejecting the premises
[Rejecting P2] Corporal punishment can be administered evenhandedly.