I was trying to mock one of my friends saying "Unlike you, I do not have this trait" but then I thought, I should have said "Like you, I do not have this trait". Till now, it seems to me that both are correct. The first one expresses that "you have this trait but I do not have" and the second one expresses "I do not have this trait like you have".

So am I correct in this interpretation? Or is there a better way to say it?