This is usually the result of incompatible/missing libraries. If you check the OSX crash report (from the Console GUI or from ~/Library/Logs/DiagnosticReports/wireshark-bin_*.crash), you'll probably see something similar to the following:

Dyld Error Message: Library not loaded: /usr/X11/lib/libfreetype.6.dylib Referenced from: /Users/michal/Desktop/Wireshark.app/Contents/Resources/bin/wireshark-bin Reason: Incompatible library version: wireshark-bin requires version 13.0.0 or later, but libfreetype.6.dylib provides version 10.0.0

Others with the same problem have resolved the issue by performing an OSX system update (or by installing the indicated libraries from MacPorts, which you seem to be avoiding). See the posts below:

 

http://ask.wireshark.org/questions/4102/wireshark-automatically-quits-the-instant-i-open-it

http://ask.wireshark.org/questions/4528/wireshark-does-not-run

http://ask.wireshark.org/questions/4146/mac-osx-installation

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