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The entirety of their relationship, it's Izuku offering his hand to Katsuki, waiting for him to take it. It takes a long time for him to do so, because initially he misunderstands - he sees that hand as weakness, as pity, as being looked down upon, instead of the love and kindness and adoration it really represents.
As they grow, however, as Katsuki becomes a less emotionally constipated bastard and actually understands what that hand means, he's able to take it. Takes it in rivalry, takes it in friendship, takes it in love, just so happy and thankful that he has Izuku and can hold him like this. That that hand is always offered to him.
But one habit he can never break is being the first to let go. Never being the first to reach out. He's the one who determines how long they hold hands for, and whether it's just habit or his pride or some deep seated issue he hasn't been able to break, it's something that continues long after he knows just how much he loves Izuku. Not that Izuku minds; they hold hands exactly the perfect amount, he points out with a smile, and is happy to accept whatever Katsuki will give him while he works on it.
And Katsuki does try, a couple of times. His hand itches to reach out and take Izuku's, while they're walking through the mall or on patrol or just sitting together at home, but for some reason he just can't. That little switch in his brain won't flip, and while eventually Izuku offers his, and then he can take it without an issue, he hates that he can't be the one to make the first move.
But then they're fighting, and the fight goes bad. It's a combination of everything wrong that could be - they're already tired from a triple patrol, awake for almost 48 hours without a break because this shit had been coordinated to drain them; there were more villains than they had been told about, so many more; the quirks weren't the ones they were expecting, faulty intel that left them scrambling in the middle of the fight to try and regroup and find a way to win.
It was almost as bad as the League, three months of this crap all culminating in this final showdown that was targeted at just the two of them, at this attempt to bring down the Symbols of Peace and Victory.
They won, because of course they did, there was no way some shitty extras were going to make them lose. But it comes with a cost. It always fucking does.
That cost is Katsuki on his knees, one arm wrapped around Izuku to hold him as close as possible, for the first time reaching out for his hand. "Don't let go of my hand, Deku." It's an order and a plea, and Katsuki is shamelessly begging as for the first time he says those words. Because for the first time he isn't going to be the first one to let go, not this time - the wound's too deep for any field dressing to do any good, he can hear the sounds of the paramedics, little Eri (not so little anymore as a sidekick with some rescue agency) is on her way and will save the day.
Izuku just smiles up at him. Gives his hand one long, tight squeeze. For the first and last time, lets go first.
When Izuku wakes up three days later, in the same hospital where he knows half the staff by name and is on nickname basis with the others, he's not alone. Katsuki is asleep in the chair beside him, hunched over uncomfortably so he can rest his head right next to Izuku's knee. Instinctively Izuku goes to reach for Katsuki's hand, to lock their fingers together so he feels a little more grounded, a little bit less alone, but is stopped by just how heavy his hand feels.
Even in sleep, Katsuki had refused to let go of his hand.
Izuku will get the standard scolding when Katsuki wakes up. "Take better care of your shitty bones, they're already weak enough. Stop trying to be the youngest pro hero to land up in a retirement home because you can't take care of yourself after you blast off all your limbs. Stop giving me a heart attack." Just like always. And just like always, Izuku will apologize, promise to take care of himself better from now on, though they both know what the outcome will be if it comes down to himself and a civilian's life.
But unlike always, Katsuki keeps reaching out. He reaches for Izuku's hand, to caress his face, lifts him bodily from the bed so he can slide in under him, resettling Izuku in his lap so he's wrapped around him like a vine. When they leave the hospital, the moment they're both settled into the car, the agency driver pulling out to take them home, Katsuki is the first to reach out, needing to feel the heat and weight of Izuku's hand in his own.
He's still the first to let go; they both have their own litany of nightmares, more than enough to keep a therapist well paid on them alone, but feeling Izuku's hand slip from his own, as simple as it was, was probably the worst. It doesn't matter that the rescue heroes showed up literally seconds later, that Eri was able to undo the worst of it all and her mentor was able to restart his heart, less than a minute total without him. Every moment stretched beyond what he had lived, the meaning of time lost in those precious seconds that he didn't have him alive and by his side and fuck if he was ever going to experience a single moment of that again. So he still lets go first. He has to.
But he reaches out just as often now, pulls Izuku close instead of just letting Izuku reach for him, an equilibrium between them as their fingers link and bridge the gap they can't close in public.
That horrible moment might have been the first time he reached out, but it wasn't the last.