What do these slang titles mean?
On We Got Married, Taemin and Naeun were talking about how easy it was for him to fall in love, and these names were put on Taemin: 오사빠, 금사빠,

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Answer

Haha 금사빠 is a shorten version of 금방 사랑에 빠지는 사람.
It means someone who falls in love so easily. (So, in other words, fall in love so easily and give up so easily too.  Very Short love)

오사빠 is 오래 사랑에 빠지는 사람
It means someone who falls in love for a long time.
So it is the opposite of  금사빠 ^ . ^