Learn Russian: Он хотел стать то ли врачом, то ли актёром. - He wanted to become either a doctor or an actor.

Using или ..., или ... simply states that his options were between those two professions. By using то ли ..., то ли ..., the speaker is adding their own uncertainty. It implies: "He wanted to become either a doctor or an actor, but I can't remember exactly which one it was."

Why are the words врачом and актёром in the instrumental case?

They follow the verb стать (to become). When you talk about professions, roles, or states someone is transitioning into after verbs like стать or быть (to be), Russian requires the instrumental case.

Could we use ли ..., ли ... without the то here?

No. While ли on its own is used for indirect questions (meaning "whether" or "if"), the specific pairing то ли ..., то ли ... is a fixed conjunction used specifically to indicate the speaker's doubt or memory lapse between two possibilities.

Why is there a comma before the second то ли?

Russian punctuation rules dictate that when you use repeating conjunctions to connect items in a list (like то ли ..., то ли ..., или ..., или ..., or и ..., и ...), you must place a comma before the second element.