Step 1: Meaning of the word "queer."
"Queer" is often used to describe something strange or odd.
Step 2: Analysis of the options.
Sincere refers to something genuine or heartfelt, unrelated to "queer."
Peculiar means strange or unusual, which aligns with the meaning of "queer."
Arbitrator refers to a person who resolves disputes, which is unrelated.
Severe refers to something harsh or intense, which is not the meaning of "queer."
Step 3: Conclusion.
Thus, the correct answer is Peculiar.
Final Answer:
\[
\boxed{\text{Peculiar is the correct answer.}}
\]