Strictly speaking, it is extremely rare for latency on a non-trivial path to NOT be asynchronous.
The only way for latency in both directions to be both equal and stable is if the bit rate of all links in the path are identical, the IP routing in both directions is identical, the traffic flow in both directions is identical, the routing policies at every device in the path in both directions is identical, and the host systems at both ends are behaving identically.
In practice, some paths will be "more" synchronous than others. Latency in two directions on a path may be approximately equal some of time if the various factors happen to balance at that moment. But that is not a stable condition as it depends on a lot more than just path itself.
Not only can latency vary by the path and traffic, but also on how you measure it. ICMP, UDP, and TCP packets may be routed differently, receive different queuing priorities, or be subject to different firewall rules. Latency is also effected by what goes on in the sending and receiving nodes.
I have written an article on the vagaries of network statistics which may be helpful: Loss, Latency, and Speed