This is only my second Discovery story. You don't have to read the first one to read this. But the end of this references that one if you squint. Kudos and comments are love.

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Disclaimer: Hello Dearies. I do not own Star Trek Discovery. I wish I did for more then one reason.

Pike knew there was a back story. There was always a backstory. Of course Michael's history was well documented. She had been orphaned at a young age when her parents were killed by rogue klingons. She was adopted by the Vulcan ambassador Sarek and his human wife Amanda. With her adoption she gained not only a new set of parents, but an adopted brother as well, Spock. Pike was very familiar with Spock, but Spock didn't speak much of his parents or his sister aside from the fact that his father is the ambassador, his mother is human, and his sister is smart and a commander in Starfleet.
After she grew up Michael joined Starfleet and worked her way up, quickly, through the ranks and served as the first officer on the USS Shenzhou under Captain Philippa Georgiou. Due to an extreme case of being in the wrong place at the wrong time, Michael was faulted with starting the war with the Klingons and was found guilty and declared Starfleet's first mutineer. Somehow, while in the course of serving her sentence, Michael had found her way onto the USS Discovery, serving as a science specialist under Captain Lorca. When Pike went to look into how that had happened he was met with a lot of redacted information. He kept at it though and pieced together small fractions of Michael's work while on the Discovery when he came to a complete blackout about how Captain Lorca was killed and how it involved retired Captain Georgiou (who Pike had heard rumors of being dead).
Pike didn't really know how to explain his fascination with Michael Burnham. In truth he wasn't quite sure if his fascination was simply with her or if it partially stemmed from having known her brother, Spock. Spock was a very private man. It took the war and Michael's sentencing for Pike to even learn that Spock had a sister. Which he only found out because he heard that Sarek and Amanda had been present, as her parents, at Michael's trial. Spock really couldn't have denied her existence even if he wanted to.
Yet, Pike was pretty sure he was fascinated with Burnham all due to her own merits. Somehow, this woman who had a rough start in life had worked her way up. And when life knocked her down, to being a mutineer, she managed to work her way right back up and earned her title and reputation back. Along with several commendations for ending the war that Starfleet had accused her of starting. So, yes Pike was pretty sure he was fascinated with Michael because she was an interesting person. Now if only he could get more information on her. Especially, concerning her time on the Discovery while serving under Captain Lorca.
Pike figured the best person to ask was Commander Saru. Not only did Saru serve under Burnham on the Shenzhou, but she then served under Saru when she came on the Discovery. Now Pike knew that many of their missions and files had been redacted, but as a Starfleet captain, Pike had some pull, and if he told Saru that he was concerned about Michael continuing on the Discovery, he knew that Saru would give him answers. In the end it didn't take much to get Saru to open up about Commander Burnham's time on Discovery and on Michael Burnham herself.
Michael's childhood was far from troubled, it was absolutely horrible. After her parents were violently murdered, while Michael hid in the closet, she was adopted by Sarek and Amanda. At first it seemed like her life would only get better from there, but that would be incorrect. A rogue faction of Vulcans did not like that Sarek had a human and a half human in his household. Unfortunately (or fortunately for Spock) Michael was the target of their bigotry. They bombed the learning center where she was a student. According to what Saru had learned from Tilly, Michael had been dead for three minutes before her adoptive father was able to bring her back by performing an unique ceremony, joining his katra to her. Pike didn't quite know how one was supposed to accept that a human shared a soul with her vulcan father, but who was he to judge or question.
Saru then shared how Michael was originally on track to join the Vulcan Expeditionary Group, but Sarek had chosen to have Spock attend. Of course Pike knew that Spock had chosen not to join that group so it seemed all a moot point anyway. Sarek had introduced Michael to Captain Philippa and from there Michael had been a part of Starfleet. Michael was then groomed to become the captain of her own starship when the time finally came.
Pike knew everything about Michael up to how the prison shuttle she was on showed up on Lorca's proverbial doorstep. Saru was a wealth of information from there. Supposedly, Michael's prison shuttle (which she was on for a still unknown reason) needed an emergency rescue. Lucky for her, the USS Discovery was nearby and took on the four prisoners and the injured pilot. From the get go Lorca had taken an interest in Burnham, according to Saru. He watched her constantly and was intent on having her join the crew of the Discovery. Saru had been privy to some of the holographic conversations that Lorca had with Starfleet command about how he needed Burnham and had the right to recruit her, by any means necessary, if it was thought she could be an asset in winning the war against the Klingons. That sounded almost reasonable to Pike until he heard that Lorca's interest in Michael was not very innocent.
It took a bit of plying and some lying on Pike's part, but he finally convinced Saru to share what he knew about Lorca and his interest in one Michael Burnham. Apparently, Lorca was not from their universe. A stretch, but Pike could believe it. However, apparently Michael (from Lorca's 'mirror' universe) and him had had an intense relationship and she had died in their universe. So, when Lorca found himself in their universe, one of the first things he did was track down the love of his life, Michael Burnham. However, this Michael had no idea who this man was. So Lorca had her join his crew and slowly he gained her trust. He followed her advice and helped her in her own personal pursuits whenever he could. He even let her and one Ash Tyler get close to each other, despite Lorca's own personal interest in her.
Now Ash Tyler was his own conundrum. Apparently, he was a real bonafide Starfleet officer until he was taken hostage by the Klingons. They learned all they could about Tyler and Starfleet. Then they took their torchbearer, Voq, and performed procedure after procedure on him till he looked like Tyler and had all the memories of Tyler. Basically Voq became Tyler and Voq's personality became almost a duel personality, waiting to be unlocked. Then when he was unlocked he reeked havoc on Michael and everything around them. Nobody was safe, not even Michael who Tyler's personality had fallen in love with. Pike was disgusted as Saru recounted all that had happened to Michael at the hands of Tyler/Voq. But that disgust had nothing on what Pike felt toward Lorca.
Even before Michael and Tyler began their relationship, Lorca had become an open ear for Michael to talk to. Anything that was on her mind or concerned her Lorca was more then happy to listen to her and to be the voice of reason, or unreason, thought Pike snidely. But once everything with Tyler went down, Michael leaned on Lorca even more. He became the understanding, indignant man in her life and Pike found that despicable. Lorca took advantage of Michael's weakness and had her eating out of the palm of his hand. In fact had someone, who Saru vehemently refused to name, hadn't stepped in and killed Lorca, Pike would have bet his commission that Burnham would have tried to bring Lorca back to stand trial. And Lorca might have actually come with her. Apparently, in the end Lorca had actually turned against some of his followers to save Michael. Despite all his dastardly deeds, at least Lorca had the decency to protect Michael and keep her from dying needlessly because of his manipulations.
Pike listened to everything that Saru had to say and his heart went out to Michael. She had not had an easy life and it seemed she had to fight for everything she had. Everything she earned she had to work just to maintain it. And around every corner were people who compromised her for their own gains and goals. Luckily for Michael she had managed to find a home on Discovery separate from Lorca's guiding hands. Saru, who admittedly had not trusted Burnham when she first got on the Discovery, quickly remembered their friendship from the Shenzhou and they formed a much stronger bond. Then there was Lieutenant Stamets, who had a hard exterior to crack, but once Michael had he had accepted her whole heartedly and looked to her when problem solving. With Lieutenant Stamets had come his partner Dr. Culber, who Pike learned had been murdered by Tyler/Voq. Dr. Culber and Michael had apparently had many a conversation about xenobiology. Of course, when listing the close friends of Michael Burnham, no one could leave out Ensign Silvia Tilly, or Tilly to everyone. Tilly had a way about her that accepted no defeat no matter the situation. If she wanted to be your friend, have you open up to her, or catch an asteroid using a very expensive starship, there was no way to say no to her. And to be fair most of her ideas were brilliant. When Pike first came on Discovery they were having trouble communicating because the Enterprise's systems were down including communications. Tilly had been the one to have Discovery request that the Enterprise switch to morse code to communicate. It spoke of their friendship that Michael chose to continue rooming with Tilly despite being entitled to her own suite as a commander.
So, Pike decided that, yes, he was fascinated by Michael. And, yes, it was for who she was and not who her brother was to him. Also, if it was at all in his ability, he wanted to be a friend to one Michael Burnham. Someone she could talk to and lean on and not worry that he was gonna turn on her or become a virtual stranger from a mirror verse. And if perhaps one day they could be something more, well he was going to keep that thought to himself. Especially, since he noticed that Stamets, Tilly, and Tyler were giving him curious looks whenever him and Michael even had a conversation. Gossip on this ship was dangerous and perceptive.