DaVinci Resolve 14 cant run my mac. Why?

The home screen starts and then closes itself
Software 10.13.6 High Sierra
Ram 8 GB
Processor: 2,4 GHz i5
MacBook Pro 2010 mid

Take a look at the minimum required specs for installation listed on the downloads page for Resolve.

Also, it could be the result of an operating system that's never been maintained. Download and run ALL the maintenance routines in ONYX for mac. https://www.titanium-software.fr/en/onyx.html

Make sure to download the version that matches your OS.

Then reboot and try restarting Resolve. If that doesn't work you may need to submit a trouble ticket IF you're using the Studio version.

There's lots of troublshooting tips here on the forum, so a search and see what matches your issue.