What a canonical tag does
It names the preferred address for a page whose content is reachable at several URLs. With and without www, with and without a trailing slash, with tracking parameters attached, a print version, a filtered category view — all of these can serve the same content at different addresses.
Without a canonical, Google decides for itself which to index, and it does not always choose the one you would. Worse, the signals from links pointing at different variants get split across them instead of concentrating on one.
A self-referencing canonical — a page pointing at itself — is what most pages should have. It is not redundant: it settles the question for every parameter-laden variant of that URL that anyone ever links to.
The failures that hide
A canonical pointing at a page that 404s. The tag looks perfect in the source and does nothing, because the target does not exist. This tool fetches the target, which is why it can tell you.
A canonical chain: page A canonicalises to B, and B canonicalises to C. Google does not follow chains and treats the middle signal as unreliable, so A may end up indexed, dropped, or consolidated somewhere you did not intend.
Two canonical tags on one page, which happens whenever a theme and an SEO plugin each add one. Google discards both when they conflict, leaving the page with no canonical at all — and the source looks fine unless you read it carefully.
And the conflict Google documents explicitly: noindex together with a canonical. One says treat this as the original, the other says do not index it. The outcome is unpredictable, and the correct fix depends on which you meant.
The header nobody checks
A canonical can be declared in an HTTP Link header as well as an HTML tag. This is the standard way to canonicalise a PDF or an image, which have no head to put a tag in — and it is also something CDNs and server configurations add without anyone noticing.
When the header and the HTML disagree, you have given Google two contradictory instructions from the same page. Its documented behaviour with conflicting signals is to treat them as unreliable, and it may honour neither.
Practically no free checker reads the header, because it requires a server-side fetch — a browser cannot read another site's response headers. That is exactly why this tool sends the request from our server rather than yours, and the page says so plainly rather than claiming to run locally.