Learn Hardcore Turkish: O iyimser kalmayı seviyor, oysa kardeşi biraz kötümser düşünüyor. - She likes to stay optimistic, whereas her sister thinks a bit pessimistically.

iyimser olmayı seviyor: likes being/becoming optimistic (in general).
iyimser kalmayı seviyor: likes staying optimistic (maintaining that state, often despite challenges).

Oysa means "whereas/however," introducing a contrast between two clauses. It often signals a stronger, more pointed contrast than ama ("but"). Halbuki is very close to oysa, a bit more conversational. You can also use oysa ki for a slightly more emphatic/literary feel. It typically appears at the start of the contrasting clause: "..., oysa ...".

Is that second o actually the pronoun again?

No. In "..., oysa ...", that o is just part of the single word oysa. There’s only one pronoun o in the sentence.

Do we need to keep the pronoun o at all?

No. Turkish is pro‑drop. You can say "İyimser kalmayı seviyor, oysa kardeşi biraz kötümser düşünüyor." The -yor ending already shows 3rd person singular.

Does o mean "he" or "she"? How do we know?

O is gender‑neutral ("he/she/it"). Context supplies gender if needed. Likewise, kardeşi means "his/her sibling" without specifying gender.

Why is it kalmayı and not kalmak after seviyor?