It all depends on how you interpret "opposite." This is a language issue, not a logic problem.
For example, what is the opposite of "hot?" Cold? Ugly? Calm? How about the opposite of "right?" Left? Wrong? Topple? Depends on the context.
In the case of your question, "what is the opposite of sing loudly," I could talk softly, keep quiet, sing softly, and they would all be correct, according to my interpretation of the term "opposite."
If you want a true logical conundrum, consider this problem:
You are captured by a race of cannibals that wants to kill you and eat you. However, they like to toy with their victims before they feast, so they tell you this: Make a single statement (yes, these cannibals speak English and love logic puzzles. Sue me). If your statement is the truth, they will stone you to death, and eat you. If it is a lie, they will burn you to death, and eat you. If it cannot be determined whether it is a lie or the truth, they will let you go. What do you say to save yourself?