Why don't links that I click on a web page open?

See some articles Clear your browsing history in Safari on Mac - Apple Support

Safari troubleshooting on Mac - Apple Support

If you can’t open a website in Safari on Mac - Apple Support

In correct DNS server settings is also a cause see this article Non-responsive DNS server or invalid DNS configuration can cause long delay before webpages load - Apple Support

Enter in user library macOS Sierra: Library folder

Delete the contents of folders Caches , Cookies , Saved Application state , Safari into the trash .

Make sure , in safari preferences > extensions is as off , in users and groups > login items are kept as empty .

The last step is delete com.apple.safari.plist from the preferences folder of user library and you have to reset the home page once again by filling up the credentials like search engine again see this article Set your homepage in Safari on Mac - Apple Support

Note : third party add ons , unwanted apps / softwares , any junk cleaners , find my files ( something like that ) , anti virus will corrupt safari .

Basic steps like safe mode is also to be run .

Here are some troubleshooting steps to follow, in no particular order:

• If Safari doesn't load a page or webpage items are missing - Apple Support
• If Safari is slow, stops responding, quits unexpectedly, or has other issues - Apple Support
• How to use Internet plug-ins in Safari for Mac - Apple Support
• "Safe Mode": Use safe mode to isolate issues with your Mac - Apple Support

  Determine if the problems exist in Safe Mode. Then, restart normally.

Needless to say, if you are using any non-Apple "anti-virus", "cleaning", or "Internet security" products, anything at all in that broad category of utterly useless garbage, don't. A lot of things won't work if you do.

If you don't get anywhere, you can use the following procedure to determine if the problem is internal or external to your Mac. Causes may involve your router, your ISP, the DNS Server(s) it uses, or certain user-configurable options.

1. Shut down your Mac.
2. Load macOS Recovery by holding ⌘ and r (two fingers) while you start your Mac with a third finger.
3. At the macOS Utilities screen, release those two fingers.
4. Choose Get Help Online.
5. Safari will launch, but it will lack your bookmarks, favorites, history and other preferences.

Determine if the problem persists while using Safari in that mode. After that, restart your Mac normally, and reply with your observations.

You are welcome .