Your screen shot shows "On My Device" - there's nothing surprising about that. It's on your device. So near, and yet so far...
This has been true since the beginning of the iTunes Store. Record labels did not want people to use their highly portable iPods (and later iPhones) to copy the contents of their libraries onto other people's computers. Remember, that was when Napster was the record industry's sworn enemy, and the labels weren't about to agree to anything that might allow copying/sharing. Apple locked down the functionality of iTunes to satisfy those fears.
Syncing is essentially a one-way street when it comes to music - music that's present on the computer can be synced to the iPhone/iPod. When you setup a new Mac, there are basically two sanctioned ways to get the music onto that new Mac - copy the iTunes library from the old computer, or download the music to the computer from the Purchased section of the iTunes Store.
Yes, after the first time you sync a particular device to that computer, subsequent sync attempts with that device may give you the option to transfer new iTunes purchases on the device over to the computer (provided both are signed into the same iTunes account). But the first sync... no way.
All that said, Apple now provides other ways to do this, unless you have a traditional iPod. Syncing of iOS devices is not necessary, if you take advantage of Apple's cloud services (some free, some paid). A combination of iCloud Music Library (formerly "iTunes in the Cloud"), iTunes Match, and/or Apple Music can make syncing of music unnecessary.
