On a WordPress website, WordPress SEO plugin by Yoast creates this weird canonical link. Basically the website name is www.test.com and when I inspect the webpage at www.test.com it shows me this link:
<link rel="canonical" href="http://www.test.com/">
This looks completely wrong to me, because canonical should be the same content on different URL but the URL is the same!
It sounds like you are a bit confused about canonical tags.
Yes you can use the canonical tags on a page with duplicate content to reference a different 'main' canonical page, but you can still use canonical tags on their own page referencing themselves.
This can help with any unforeseen or future canonical issues that may arise, or combat duplicate pages in instances such as:
http://test.com/
http://www.test.com/index.php
The pages above are the exact same page as http://www.test.com/, but accessible without www prefix and with trailing index.php file.
Here is a video by Matt Cutts from Google on this exact subject.
