The intriguing question of why Spock never mentions his adoptive sister, Michael Burnham, throughout his tenure in Starfleet is a curiosity that has been addressed in the second season finale of "Star Trek: Discovery". It's a matter deeply intertwined with a critical moment in the series when the Discovery crew made the weighty decision to travel into the future. Their mission was to safeguard the sphere data, an immensely vast repository of knowledge, from falling into the hands of Control, a rogue AI threatening to wreak havoc across the universe.

Following this dramatic event, an in-depth debriefing was conducted by Starfleet. During this process, several members of the Discovery crew, including Tyler, Spock, Pike, and Number One, were questioned about the circumstances surrounding the crew's decision and the subsequent impact on Starfleet's operations. It was a rigorous inquiry, considering the gravity of the situation and the potential implications for the future of Starfleet.

During this debriefing session, Spock found himself proposing a rather bold and unusual suggestion to the Starfleet officer conducting the debriefing. In an effort to shield Starfleet's past and future from any potential threats, Spock proposed that all files, documents, and data pertaining to Discovery's mission, its diverse crew members, and the groundbreaking yet controversial spore drive technology, should be classified and sealed.

Spock's proposition didn't stop there. He also recommended that any Starfleet officer privy to these events, whether through direct involvement or access to information, should maintain absolute secrecy. This silence was to be enforced under the severe penalty of being charged with treason, a crime indicating a betrayal of Starfleet's trust and its principles.

Spock's recommendations were eventually adopted, a testament to his influential position within Starfleet and his reputation for sound judgment. It is this secrecy protocol, necessitated by extraordinary circumstances, that provides a credible explanation for Spock's persistent silence about Michael throughout his illustrious Starfleet career.

By accepting these measures, Spock consciously chose to withhold the information about his relationship with Michael Burnham, irrespective of the personal significance it held for him. His decision demonstrates his unswerving commitment to Starfleet's broader mission and the lengths he was willing to go to protect the organization's integrity and its future. It highlights the character's ability to prioritize the greater good over personal attachments, providing a deeper understanding of Spock's personality and the choices he makes during his Starfleet service.