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While the exact nature of copyrights in a particular country depends its copyright laws, in many places you cannot copyright a phrase because it does not constitute a sufficiently original work. In the US, for example, you can only copyright a work that is original and constitutes a creative work of art or similar creation. A poem, though often short, is protected under copyright due to its function as original art that expresses an idea in a unique or new manner. You cannot copyright a phrase because, essentially, it is not artistic or creative, though you can potentially protect a phrase through other methods.
Copyright laws in the US, and other countries such as the UK, provide protection for original creative works and artistic expressions. This work must exist in a somewhat tangible form, such as written, typed, sculpted, or recorded, to establish its singular form. You cannot copyright a phrase due to the fact that the phrase likely does not represent a new work in its entirety. If you wanted to copyright a phrase that is part of an artistic work, you would be unable to do so, though the entire work would be protected by copyright.
This is similar to the fact that you cannot copyright a character name or the title of a work of art or creative expression. A copyright represents ownership over intellectual property in the form of an artistic work. You cannot copyright a phrase because a phrase does not inherently represent an artistic work of creative expression. If you were to write a short poem that was essentially identical to a phrase, then you would have protection of your poem under copyright, though you cannot copyright a phrase itself. This protection would cover the poem, but not other uses of that particular assembly of words in ways that do not represent similar works of art.
While you cannot copyright a phrase, you can protect a phrase by other means in certain situations. If you wish to use a particular phrase as an identifier in business for a particular company, product, or service, then you could protect that phrase by different means. In general, you would want to register the phrase for protection as a trademark or service mark. This would protect that phrase for use in commercial applications, but would not grant copyright protection to you for that particular phrase.