Jawaban:

I think both options works, depending on the context.

1. "What do you mean?" digunakan saat kamu belum paham dengan penjelasan lawan bicara.

2. "What did you mean?" digunakan saat kamu sudah paham dengan penjelasan lawan bicara, tetapi hendak memastikan atau mengklarifikasi penjelasan yang baru saja kamu dapat. Some people said this option sounds more polite as well.

Both options works, though.

Untuk situation temen ngejelekin diri sendiri, I think the second option is more proper.

If we use DO, it's as if you confirmed that the things your friend have said about themselves are true.

On the flip side, if you use DID, you basically deny the things that your friend have said about themselves.

Also, it seems like you're using the word "like" incorrectly. I suppose you meant to say "seperti" but the word "seperti" doesn't translate to "like" in this context. Instead, say "why did you say such things (about yourself)?" atau "why would you say that (about yourself)?".

Sorry for using English and B.Indo back and forth, I hope it's understandable :")