While using Safari, when I want to go to a website, I am prompted to allow Facebook. They error I get is, "Safari can't verify the identity of the website "www.facebook.com". I always hit the cancel key, and eventually make it to the website I am trying to get to. But, why is it always trying to take me to Facebook in the first place?

When I am trying to open non-Facebook websites, I am constantly getting this certificate error while using Safari:"Safari can't verify the identity of the website "www.facebook.com". The certificate for this website is invalid. You might be connecting to a website that is pretending to be www.facebook.com, which could put your confidential information at risk. Would you like to connect to the website anyway?It appears that I am being redirected to Facebook. Is this a Safari quirk, or is this a virus?

That is something Facebook put in place to let people know they were leaving Facebook and the link they clicked may be a virus, keylogger etc.

This person isn't leaving Facebook.
I think it's a site posing as facebook which you have allowed on without realizing it.
Look in your list of programs and see if you have two facebooks, one of which is slightly different, and see if you can remove it.