Is the goal to directly sound smarter or is it to quote something in another language, which may come off as showing off?

Because there's a difference between quoting something and conversing in said language.

For example, English is often quoted by foreign speakers, usually in things that are said in English: "My fellow Americans, ask not what your country can do for you, ask what you can do for your country." It's an iconic, memorable line and people remember it and quote it in English, even if they speak another language. The same is done for Latin or Greek works.

Some people quote works in their original language to show their familiarity with the works in its original form.