In Asymmetric routing, a packet traverses from a source to a destination in one path and takes a different path when it returns to the source.
In Cisco ASA/Pix firewalls, state information is built when the packets flow from a higher security domain to a lower security domain. The firewall will be an exit point from one security domain to the other. If the return path passes through another firewall, the packet will not be allowed to traverse the firewall from the lower to higher security domain because the firewall in the return path will not have any state information. The state information exists in the first firewall.