Atrevería comes from the verb atreverse, meaning 'to dare' or 'to venture'. It's a strong word that conveys confidence and boldness.
In "Te Conozco Bien," Marc Anthony repeatedly uses this word to emphasize his certainty about his ex-lover's feelings and future actions. He sings, "Me atrevería a jurar" (I would dare to swear), highlighting his unwavering conviction that she will return to him. This word captures the song's central theme of knowing someone so intimately that you can predict their every move.
"Te Conozco Bien" is a salsa song about an ex who left, but who the narrator is convinced isn't really happy where she landed.
He feels sorry for her, and a little angry too, because he gave her everything and she still walked away for someone else. But he knows her too well to believe it's over. He hears it in her voice when she calls, and he's sure she's not happy with her new partner, even if she pretends to be.
So he waits. He's confident she'll come back, knock on his door, and admit she made a mistake. The chorus repeats that certainty like a promise he's making to himself: "I know you well, and you'll come back."