Since the Halloween update dropped for Overwatch there has been an annoying bug with watching highlights.
Players wanting to watch highlights would find themselves being confronted with the “Client Requested Disconnect” message. The only way to get around this was to start a custom game on the same map as the highlight you wanted to watch then leave the game and watch the highlight.
Blizzard is aware of this issue and says that a fix is coming tomorrow (Tuesday 18th) and it’s being tested right now.
Fingers crossed this is sorted out, it’s been a problem for nearly a week.