Warning! The following contains spoilers for the Season 2 premiere of Star Trek: Discovery. Read at your own risk!
Star Trek: Discovery exploded into Season 2 with an action-packed premiere, and while Spock didn't appear in person in the present, we learned a lot about where he was in life. We also learned quite a bit about his relationship with Sarek, as well as how close he is to his sister, Michael Burnham. We don't know the full story just yet, but we learned enough to possibly understand why Spock never mentioned her in other Star Trek adventures.
We first see them interact in a flashback after Sarek and Amanda agreed to take in Michael and raise her Vulcan alongside Spock. After some awkward introductions, Sarek and Amanda take her upstairs to meet Spock. The young Vulcan doesn't acknowledge her presence at first, choosing instead to focus on a drawing he was creating on a screen that made holographic images. Eventually, he gets up, only to reject Burnham's handshake and slam his bedroom door in her face.
In the present, Sarek confessed he had an ulterior motive in fostering Michael Burnham in her youth. While raising her Vulcan was beneficial to Burnham, Sarek hoped that her presence would teach Spock to learn empathy. He confessed that he believed the lesson never took with his son, but Burnham disagreed. She knew Spock was capable of empathy, and Sarek sensed there was a story to tell behind that statement. Still, he didn't press any further.
As for what that story was, Star Trek: Discovery fans were left to wonder for a spell, and even then they really didn't learn exactly what happened that prompted Michael's response. They did learn, however, that she takes the blame for Spock's distance from her, and why they haven't spoken in years. Burnham informed the charming Captain Pike she wished to travel to the damaged Enterprise, presumably in hope of making amends with her foster brother.
In what was a surprise to Burnham, but to no one who's watched the trailers for Star Trek: Discovery Season 2, Spock wasn't on the Enterprise. He's gone on leave to search out the meaning of the red dots, and after nearly losing her life at the cost of chasing one, Burnham is very concerned he's in great danger. The episode ends with Burnham focusing on Spock's map, and praying that she doesn't "lose him again."
The trailer that followed the episode shows that Michael Burnham will reconnect with Spock at some point down the road, but will the two reconcile? Obviously, he never made mention of her in "future" Star Trek adventures, so it would canonically make sense for Spock to hold a grudge. That said, Vulcans have a tendency to avoid discussions about family, so it may be no one on the Enterprise ever asked about her. We'll see what happens later this season.