Just to follow up, I am still having this problem. There are no antivirus or security applications running or installed. No firewall, no anti-malware, nothing. I've completely removed Calibre as far as I can tell. Is there more than the Calibre app to delete? I didn't find anything else. I reinstalled it using the latest version, 5.7.2. I've moved the books and database so it should be starting from scratch and not trying to load them. Yet, consistently it gives me these lines in the system log not long after start.
Dec 17 20:34:54 My-Computer-Name com.apple.xpc.launchd[1]: Coalition Cache Hit: app<application.net.kovidgoyal.calibre.12933608386 .12933608513(501)> [10200]
Dec 17 20:34:56 My-Computer-Name calibre[6050]: getattrlist failed for /System/Library/Extensions/AppleIntelHD5000GraphicsGLDriver.bundle/Contents/MacOS/AppleIntelHD5000GraphicsGLDriver: #2: No such file or directory
Dec 17 20:34:56 My-Computer-Name calibre[6050]: getattrlist failed for /System/Library/Frameworks/OpenGL.framework/Resources//GLRendererFloat.bundle/GLRendererFloat: #2: No such file or directory