"Farewell, ungrateful traitor!" begins with an abrupt ending. In no uncertain terms, a female speaker tells her dishonest boyfriend that she's done with him for good.
In fact, she says so twice:
Farewell, ungrateful traitor!
Farewell, my perjured swain
Her anaphora on the word "farewell" here makes her point crystal clear: this "perjured swain" (or lying lover) can go ahead and get out of here, and he shouldn't let the door hit him on his way out.
While this speaker is obviously furious, she's also heartbroken. If her "swain" is a "traitor," her "farewell" comes after he's already betrayed her trust and, it's implied, moved on with someone else. He's said "farewell" to her before she can say goodbye to him.
Having begun with a direct apostrophe to her cheating lover, the speaker suddenly broadens her critique. It's not just her "perjured swain" who's a liar and a cheater, she says: it's every man in the world. No "injured creature"—that is, no betrayed woman—should ever "Believe a man again" if she knows what's good for her. In other words: this is going to be a poem not just about how one man cheated on or abandoned one woman, but about how every man is a no-good, lying jerk. This is the furious lament of a woman in pain.
These opening lines establish the poem's meter as a mixture of iambic tetrameter and trimeter (that is, lines of either four or three iambs, metrical feet that follow a da-DUM rhythm). Take lines 1-2:
Farewell, | ungrate- | ful trai- | tor!
Farewell, | my per- | jured swain
This short, bouncy rhythm makes the lines feel both energetic and curt. But, as readers can see above, the first line isn't actually full tetrameter: line 1, like all the odd-numbered lines in the poem is, catalectic, which just means that it's missing its final expressed stressed beat. This adds playful variation to the poem's rhythm.