I'm on OSX version 10.14.3 (18D42). I've seen the other post about making sure you're an admin user and allowing apps from identified developers and right clicking on the application but after going through all of that TT still won't open. I see it show up as a process for a few seconds then it disappears so I assume it is shutting down because of some error. Here's some logs:
default 15:29:17.408225 -0600 loginwindow -[PersistentAppsSupport applicationReady:] | App: TurboTax Deluxe 2018, ready, updating active tracking timer
default 15:29:17.408287 -0600 loginwindow -[ApplicationManager checkInAppContext:refCon:eventData:] | checked in app : TurboTax Deluxe 2018
default 15:29:18.524395 -0600 loginwindow -[PersistentAppsSupport applicationQuit:] | for app:TurboTax Deluxe 2018, _appTrackingState = 2
default 15:29:18.524421 -0600 loginwindow -[PersistentAppsSupport applicationQuit:] | App: TurboTax Deluxe 2018, quit, updating active tracking timer
error 15:29:21.395160 -0600 ReportCrash File creation failed TurboTax 2018_2019-01-26-152921_Macusers-iMac.crash - uid: 503 gid: 20, euid: 503 egid: 20 - error 13: Permission denied
error 15:29:21.395239 -0600 ReportCrash Failed to save crash report for TurboTax 2018[1058] (version 2018.r13.036 (2018.r13.036)) to TurboTax 2018_2019-01-26-152921_Macusers-iMac.crash.
I wonder if the permission denied is the reason it is quitting or it is denied creating a log/crash report. As previously mentioned I am the admin user on this computer.
Here's my story. Spent hours and hours working on my taxes on Home and Business version of TT. It crashed over and over. I had to re-do the taxes several times. Finally after saving the document in 10 locations and countless hours of doing my taxes. I got to the end. And the return would not e-file or print. Spoke to support for hours. Literally hours and they could not fix the issue.
I got a refund. Downloaded HR Block software and while watching my 2 children under 2 i was able to complete my taxes in a few hours.
If you are having issues with the program crashing, files being corrupt. Stop. Get a refund. And go to HR block.