My husband and I were discussing "School Reunion" last night, as is our wont, because that episode is gorgeous and surprisingly deep. During our discussion, I thought of something and asked him, "Why did the Doctor allow Mickey to join the TARDIS team when Rose told him not to?"
In case you don't remember the exact scene, this is what happened:
The Doctor invites Sarah Jane to accompany him again, and she refuses. Mickey pipes up, "Can I come? No, not with you, I mean with you. Because I'm not the tin dog, and I want to see what's out there." While Sarah Jane encourages the Doctor to say yes, that he needs a Smith on board, the camera is on Rose with Mickey behind her where he can't see her face, and she looks at the Doctor and mouths an angry "No!" to him. He eyes her for a moment, then says to Mickey, "Okay then, I could do with a laugh." Mickey asks Rose, "Rose, is that okay?" and she replies, sulking, "No, great. Why not?"
Thus the question: Why would the supposedly Rose-besotted Doctor go against her direct order and say yes?
We came up with a few explanations, though I'm not sure which is the most likely. The first is that by this point, the Doctor has started to respect Mickey, mostly for his abilities and his loyalty (but maybe also because Mickey's been able to turn his back on Rose and take his life back?), and he's always willing to take on a companion that deserves the chance. Okay, that's a bit weak (not the Mickey being awesome part, but the second part), but if you combine it with the idea that the Doctor isn't completely besotted by Rose, it works.
(And, while I do agree that the Doctor loved Rose, I do not believe that he was single-mindedly obsessed. Sure, he made many stupid mistakes because of her and later on pined for her, but his life did not revolve around her, not like Eleven-Amy or Twelve-Clara.)
My theory is that he defied Rose's order in retaliation for her behavior earlier in the episode. When Sarah Jane arrived on the scene, Rose kicked into high jealousy, unwilling to believe that the Doctor could have had any previous relationships and then being outright hostile to Sarah Jane. Then when the Doctor, for once, and probably for the only time ever with Rose, poured his heart out to her, telling her about the difficulties of his life, she barely listened, then brushed him off as she tried to manipulate him into saying he loved her. If that's how she's going to treat him and his friends, why should he do what she says? And having Mickey around is going to punish her more than it punishes him.
My husband's theory is that encountering Sarah Jane again reminded him that Rose runs on emotion and is neither intelligent nor wise. Sarah Jane is the one investigating the school and figuring out that something is wrong; Rose is just fuming that she had to be a dinner lady. Sarah Jane is the one trying to break into the computers; Rose is sitting there sulking (not that the Doctor saw that). Sarah Jane is the one who realizes that Brother Lassar's offer is wrong; Rose is eager to live forever to stay with the Doctor, no matter the cost. And thus, when Sarah Jane says take Mickey and Rose says don't, whose advice is better?
Honestly, though, I think it's a combination of all of it. I think that if only one or two of the reasons existed at the time of the decision, the Doctor would have acquiesced to Rose; we needed all of it for the Doctor's choice to be reasonable. For example, if the Doctor respected Mickey and Sarah Jane had vouched for him but Rose had acted maturely and demonstrated compassion to the Doctor earlier, he might have decided in favor of her. I think, though, the coolest thing about this discussion was that it exposed even more depth in this already wonderful episode.