That would be because the policy is that SW will request no one consume peanuts on a flight with a peanut allergic person. They will provide an alternate snack (such as pretzels), but SW will not stop you from bringing peanut products on board, nor will they stop you from consuming them. It is merely a request.
From the SW website:
Our CSA will advise the Operations (Boarding) Agent so that service of packaged peanuts can be suspended for that flight. Our Operations Agent will notify the Provisioning and/or Ramp Supervisor to stock the aircraft with a sufficient supply of pretzels or alternate snack. The Operations Agent will also notify the Flight Attendants of the Customers final destination and advise them that we cannot serve packaged peanuts until the Customer deplanes.
As some of our other snack items may contain peanut particles, peanut oil, or have been packaged in a peanut facility, Customers who have allergic reactions to eating/ingesting peanuts should read the ingredients on any packaged snack before consumption. Of course, all Customers are welcome to bring their own snacks with them.
Southwest cannot prevent other Customers from bringing peanuts or products containing peanuts onboard our flights. In addition, Southwest cannot give assurances that remnants of peanuts and/or peanut dust/oil will not remain on the aircraft floor, seats, or tray tables from flights earlier in the aircrafts routing.