Here's why:
* Clauses have a subject and a verb. This phrase lacks a complete verb.
* Clauses can stand alone or be part of a larger sentence. This phrase cannot stand alone and make sense.
It appears to be a fragment of a sentence, specifically missing a verb.
To make it a clause, you'd need to add a verb. For example:
* You missed the plane that was supposed to take you to the conference.
This sentence now has a subject ("you") and a verb ("missed") in the main clause, as well as a subject ("plane") and a verb ("was supposed to take") in the relative clause.