I keep getting a 'your connection is not private' message.

Edit:

Starting with "s", it is seemingly secure. So, this site is either phishing site, or you have Malware on your Mac. So, perform the following:

What to Do:

A. Don't Use this Site:

Keep off of this site, being it is seen the other way around.

And...

B. Scan for Malware:

Scan with Malwarebytes for Mac:

Malwarebytes searches for malware (short for (malicious software) and spyware. Those make your Mac act in a mislead manor. So scan with it, and remove what is found from the quarantine. It is created by longtime users of these forums making it the only reliable Security Software for a Mac. If synced with iPad connected, it may have got installed on your Mac.

Downloads:

1. Malwarebytes Anti-Malware for Mac
2. Malwarebytes Uninstaller

And...

C. Clear your Temporary Internet Files:

Boot into Safe Mode and then Clear your Temporary Internet Files of Safari:

1. Booting into Safe Mode: [hold down shift upon boot until the login screen appears]. See if this is still an issue. Safe Mode lets items run as default, without changes whatsoever. That is possible because caches of your macOS are temporarily disabled while in Safe Mode
2. Clearing your Temporary Internet Files (Cookies & Cache) of Safari: Cookies perform remembrance of certain site-entered data. Whereas Cache keeps a snapshot of the last time you visited a site.  Use this Link: Clearing History and Cache - Apple Communities

Heeelllppp678 Said:

"keep getting a 'your connection is not private' message.: I can't access many different websites. I've tried with two different browsers and it still happens. I'm running an older version OS X Capitan 10.11.6. I've tried searching this error and also tried the suggested fixes but to no avail. Any help would be appreciated. Thanks. P.S. I'm not very tech savvy at all!"

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Troubleshooting "not private" Message:

Non-Encyption is the Culprit:

If you look at top-left corner*** of your screenshot, you'll see the protocol being used in the the domain: it starts with "http" not "https". The "s" refers to the site being encrypted (secure). So, that is why you are getting this message.

***Screenshot:

Uninstall Security Software:

Seeing red-colored text, it almost seems you are using security software on your Mac. If so, uninstall it, as it just gets in the way. This is a pure example of how and why. If there is no "s" in the protocol being used, then you'll get a message right off of the application of the Mac. Important: Get the uninstaller form none other than the developer of the software, as getting it elsewhere, you may end up installing malware or other junk of your Mac. Contact the Developer, providing them with the version of the software and you macOS, requesting which uninstaller to use.