It is strange because the preview is actually displaying content that is not existed any more.
I had changed the name of one of my html pages, but didn't update the links that pointed to that page so the destinations were wrong.
After I corrected the link destinations I uploaded the changes but when I visit my site and click on the links I get an error page because the links are still trying to take me to the old name html page.
WARNING: The upgrade process will affect all files and folders included in the main Word Press installation.
This includes all the core files used to run Word Press.
There are two methods for updating - the easiest is the one-click update, which will work for most people.
If it doesn't work, or you just prefer to be more hands-on, you can follow the manual update process.
Also a deploy key cannot be used for this, as it won't trigger a build.
Source: https://help.github.com/articles/troubleshooting-github-pages-build-failures/ In my case, none of above solutions works.
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