There's a difference between running to and running from.
Olivia deserved neither.
When Elliot left her, he was reckless and destroyed. He wasn't running to the warmth and safety of his family. He was running from everything that had abruptly and expectedly burst into flame.
He was running from Liv's rejection- her fear of them and everything they could be; running from the images of blood on the floor of the squad room, from the stoic chaos of the silence that followed.
Running from psych evals, IAB and the flurry of procedures that follow a fatal shooting. He would have done it all if it meant a damn bit of difference, but as Jenna was placed in her coffin, the final nails were hammered into his own.
He was done: the blemish of the NYPD. Regardless of witness statements and extenuating circumstances, everyone knew why he did what he did.
Including Kathy.
So, he ran. But first, he imploded.
Months of drunken days, and nights passed out on the couch, sent to his mother's to "figure shit out or don't come back".
Honestly, he didn't want to go back, but he didn't know where to go instead. He failed Olivia in every way and gave her the worst version of himself when she deserved the very best. He crushed her when his heart was shattered, dealt unforgivable final blows. He didn't want forgiveness. He didn't deserve forgiveness.
Kathy was different- he could beg for her forgiveness. Not because he loved her more, but because he was the mother of his children. Nothing more, nothing less. He decided he owed it to his children to try to be the family they deserved, and he would have to put his imaginary life with Olivia to rest for good. A parallel universe where he and Olivia were together and happy, his kids adored her and their younger half-siblings, and Kathy got remarried to someone who loved her just as much as he loves Olivia.
Maybe now, things would be a helluva lot easier. Maybe if he made different choices, if they both stopped running, the present would look a lot brighter. Maybe Kathy would still be alive.
Maybe.
Regret lives under his skin, tender flesh that aches with apologies. He's done nothing but mar Olivia with his trauma since his bullish return to her world, and he doesn't know how to fix it.
He wants her to be happy, needs her to be happy and whole and safe. And if that means he needs to stay out of her orbit, so be it.
Elliot cannot and will not bruise her anymore.