Why Safari cannot open certain websites?

Go step by step and test.

1. Update Safari, if an update is available. Update may come with bug fixes.

    Update to the latest version of Safari - Apple Support

2. Force Quit Safari, launch Safari holding the Shift key down.

How to force an app to quit on your Mac - Apple Support

3. Startup in Safe Mode. 

   Start up your Mac in safe mode - Apple Support.  

    Quote:

    It also does a basic check of your startup disk, similar to using First Aid in Disk Utility. 

    And it deletes some system caches, including font caches and 

    the kernel cache, which are automatically created again as needed.

4. Clear History

    Clear your browsing history in Safari on Mac - Apple Support

    Please read the article before clearing history, 

    this is like a low level resetting of Safari without affecting passwords and bookmarks.

5. If Safari doesn't open a webpage or isn’t working as expected

    If Safari on Mac doesn't open a webpage or isn’t working as expected - Apple Support

There have been many, many problems reported here on this forum where Safari is unable to open certain web sites. To date no specific reason or solution has been offered. Sometimes updating Safari by upgrading your computer's operating system will resolve the problem. Sometimes not. It doesn't seem to happen to all Macs. What is interesting is that using another browser such as Thunderbird almost always works for those problematic sites. This is why many of us have two browsers installed.