Asymmetric routes is an obscure topic.
When they are a problem, they mainly causes disconnections and timeouts and it’s hard to diagnose, because some things work and other work for a while.
Asymmetric routes occur normally on the Internet when response packets take a different route than original request paquets. They are no problem for routers and most of the time doesn’t affect you unless you have multiple WANs and you’re somehow receiving on a different WAN than the origin WAN.
But when they occur on the lan side or intranet (like P2P VPN or MPLS) they can be a problem. Most of the time it’s because people have strange configurations with multiple routers on the same subnetwork, and a stateful firewall involved. (most modern decent firewalls)
Symptoms are disconnections of TCP connections.
Strange log entries:
UDP and pings no problem.
VoIP connects, and disconnects calls about after 2 minutes.
Sometimes one party can hear the other but not vice versa.
If you google for it, you’ll find a lot of articles, blog posts and videos about the topic. But most of the explanations are way to complicated.
This is probably the best description about the problem i have found: