Asymmetric routing occurs when traffic does not traverse the same path in both directions of a conversation.
This can cause problems when there are stateful devices, such as firewalls or NAT devices, in the path that expect the traffic to be symmetrical. Asymmetric routing can also result in suboptimal TCP performance, as TCP assumes that the SYN and ACK packets take the same path1.
To validate the theory of asymmetric routing, the engineer should run the traceroute command on both the source and the destination network devices. The traceroute command shows the route that packets take to reach a destination, by displaying the IP addresses and hostnames of the routers along the path, as well as the time taken for each hop. By comparing the output of the traceroute command from both ends, the engineer can determine if the traffic is taking different paths in each direction, and identify where the asymmetry occurs2.
The ping command is not sufficient to validate the theory of asymmetric routing, as it only tests the connectivity and latency between two devices, but does not show the intermediate hops or the path taken by the packets. The route command shows the routing table of a device, but does not show the actual path taken by the packets. The nslookup command resolves a hostname to an IP address, or vice versa, but does not show the route or the connectivity between two devices.
References: How to Find & Fix Asymmetric Routing Issues | AuvikIdentifying and Troubleshooting Asymmetric Routing in WAAS - Cisco Community