Corporal punishments cause mental scars that never heal. This can affect a person for life: making the punishment disproportionate to the original transgression.
Research indicates that people who have been subjected to corporal punishment are more likely to suffer from anxiety disorders, depression and addiction problems.  These mental disorders often stay with the afflicted for their entire lives. In this sense, the punishment is rarely proportionate to the crime or transgression. If a child is beaten for swearing, for example, the punishment can cause lifelong damage. This hardly seems proportionate to the infraction. 
The argument that the punishment needs to fit the crime is not necessarily an argument against corporal punishment. Prisons also contribute to mental disorders, including depression, yet we accept this punishment as necessary for a number of crimes and digressions.  Just because corporal punishment contributes to mental illness does not mean it should be prohibited; it just means that it should perhaps be reserved for more serious digressions.
[P1] The punishment should fit the crime. [P2] Corporal punishment leads to lifelong mental illnesses. [P3] Therefore, it does not fit the crime. [P4] Therefore, corporal punishment should not be allowed.
Rejecting the premises
[Rejecting P3] It depends on the crime. There are plenty of crimes where corporal punishment, even with its mental illness risks, does fit the crime. [Rejecting P4] Prison also leads to mental health problems but we accept this as an acceptable form of punishment.