Then ROOT behaves as it supposed. By default it shows new web-based TBrowser,
but still classical TCanvas. And If I understand correctly - you have crash when running TCanvas.
Using root --web just switches you to newer web-based canvas.
From your myRoot.txt one can see that problem is in libpng.
There are several posts on the forum having similar problem on mac:
Maybe installation of libpng and re-build of ROOT will help you.