ROSE
Look...
maybe we should go back. Let's go and find Captain Jack, he'd know
what to do.
DOCTOR
Gah, he's busy! He's got plenty to do rebuilding the Earth!
Children in Need Special
He doesn't recognise Jack at first. Perhaps because this Jack is so different from the one he knew: darker yet more open, more callow and flirty. Perhaps because it was Before Rose, and he was different too (cold, harsh, rude, scared, guilty, hates-himself-so-much, can't-bear-to-look-in-the-mirror, lost, hopeless, alone). He doesn't want to remember that time, when his life was swallowed by the still fresh scar (wound, hole, emptiness) in his psyche (his heart) where his people (his stuffy, bureaucratic, cold-hearted people whom he could never quite hate) used to live.
Even when he concentrates he barely remembers the first time he met Jack. It was in a bar in 2007. He has (very) vague memories of Jack shouting things his (very) drunken mind could not understand. He remembers waking up (on a strange couch, in a strange lounge) to the sound of voices. ("You want me to help him? He leaves me behind on a space station full of dead bodies orbiting a war torn earth, centuries ahead of my own time and you want me to help him? He doesn't even remember me!) One he does not recognise. The next voice is familiar ("Time travel, Jack. He might not even have met you yet!"): the Brigadier. He pretends to sleep as they enter the room. They never realise that he heard the conversation, he never tells them. The Brigadier (who is old, fragile, dying: it scares him) introduces them after he has pretended to wake up. The stranger (Jack) wears a smooth emotionless mask; only a brief flicker of recognition in his eyes as they shake hands betrays that this man is more than just a stranger.
A week later he is still at the Brigadier's house, sitting at the kitchen table and making a new sonic screwdriver from odds and ends he has found in the TARDIS. He tries not to think about what happened to the old one. He tries not to think about the other TARDISes (gone). He does not think about his people (his people: but he has never wanted to claim them before). He improves it: adds new settings and new functions. Jack, sitting opposite him, suggests one to reattach barbed wire. There is a glimmer of amusement in those blue eyes that he does not understand. He wonders if it is the first emotion that he has ever seen in the man. He makes an acid comment and the glimmer vanishes.
Two weeks after that, he is still on earth. He can not bear to be in the TARDIS for long. It is filled with memories (Susan, Romana, Gallifrey). He has spent much of the time wondering about Jack. Jack, who never answers any questions. Jack, who is mostly cold and silent but sometimes (just sometimes) seems to care. Jack Harkness, who is listed in one of the history books on the TARDIS as a key figure in the rebuilding of a war torn Earth. There is a picture too; it is definitely the same Jack. Jack never enlightens him.
It is Jack who encourages him to leave ("You love danger," he says. Jack has forgotten to be cold, forgotten to pretend that they are strangers. "You're no coward. Don't stay here forever.") He does leave, and begins tracing the ripples of the Time War, helping when he can, mourning when he can't. He replaces the cold, harsh rudeness with manic energy, and follows the ripples to the Nestene Consciousness, hiding in London in 2005. While he is there, he meets his salvation (Rose Tyler). She watches him in a way that makes him want to see what she sees. He looks in the mirror (A man. She sees a man. Not a murderer, not a renegade: a man).
Later, in the TARDIS (it has been infused with her light, her life) he spares one last thought for Jack (who pushed him to her. He needed that push).
After he meets Jack (After-Rose-Jack), it takes him quite some time (hours) before he works it out. There is a jagged emptiness in Jack that speaks to the (larger) jagged emptiness in him, and it is familiar. He has felt that before ("Nice to meet you," Jack's lips say, but the look in his eyes says differently) and he wondered, and he questioned, but Jack (Before-Rose-Jack) never explained.
When he realises, it is another reason to resent (not hate, never hate) this man. This man of whom Rose thinks so much ("Like you," she says. "Except with dating and dancing"). This man who is sort-of-but-not-quite the (kind-of-friend) Jack that he knew. This Jack charms him. He smiles, he jokes, he saves lives (and, more importantly, Rose's life), and he reacts with real confusion when Rose saves his life at risk to her own. He can not resent Jack. In a different way, Jack is just as dear to him as Rose is.
He watches them (his Jack-and-Rose) as they laugh and run across the frozen waves of Woman Wept. Jack has never been more different (from Before-Rose-Jack). He is lighter, happier. Rose has made this Jack, just as she (and the long-ago-Jack) made him. He's going to leave this Jack behind somewhere (he is not quite sure where) and Jack will change (grow up, grow serious, grow cold). He will break this Jack, just like he has broken so many others (Adric, Tegan, Ace, Gallifrey).
The contrast is unbearable. He turns away.