So one of the burning questions since the finale has been "Why did Spock never mention he had a sister?"
I think the answer is pretty obvious...he doesn't really consider her his sister. Vulcan logic would dictate that, to him, she is merely Sarek's ward. Not a relation to him at all. I'm sure he doesn't dislike her or anything like that. He just doesn't consider her his family. Plus remember..., he was Kirk's first officer, and they probably knew each other from Starfleet Academy, yet Kirk didn't even know Sarek was his father until Journey To Babel. Spock never brought up Burnham because...a) she wasn't really his sister...b) it was nobody's business, and...c) Spock was never one to blab about the details of his personal life anyway. In short...nobody ever asked and he never volunteered the info.
I think the answer is pretty obvious...he doesn't really consider her his sister. Vulcan logic would dictate that, to him, she is merely Sarek's ward. Not a relation to him at all. I'm sure he doesn't dislike her or anything like that. He just doesn't consider her his family. Plus remember..., he was Kirk's first officer, and they probably knew each other from Starfleet Academy, yet Kirk didn't even know Sarek was his father until Journey To Babel. Spock never brought up Burnham because...a) she wasn't really his sister...b) it was nobody's business, and...c) Spock was never one to blab about the details of his personal life anyway. In short...nobody ever asked and he never volunteered the info.