You do not have the necessary read, write and append privileges on the selected network backup disk
On my iMacs running macOS High Sierra (version 10.13.6) I had to explicitly add filesystem permissions for Time Machine to function correctly over the network. This resolved the You do not have the necessary read, write, and append privileges on the selected network backup disk error message.

I'm using username_A on both the source and destination iMacs.

On the source iMac, I used username_A when configuring Time Machine to run over the network to the shared network drive.

On the destination iMac (the one sharing out the Time Machine backup disk over my home network), I had to add username_A to the list of allowed users in System Preferences → Sharing → File Sharing. I also had to pull up the Get Info window for the shared disk and add username_A to the Sharing &amp; Permissions list at the bottom of the window. Once I had added username_A in both places on the destination iMac, I was able to get Time Machine running over the network.