Because Sherlock is so much younger, back when Mycroft was a teenager, he always held Sherlock's hand. It's just really natural to them when they walk next to each other to slip hands into the other. It's not sexual at all, but it does make others feel uncomfortable at first.
It's very strange to see them arguing over something trivial or over national security while holding hands.
It also doesn't stop people from wondering what else Mycroft has done to Sherlock consensual or not when Sherlock was younger and they wonder if they still do such things.
But of course, they didn't do anything of the sort. Maybe Mycroft used to kiss Sherlock on the forehead but now, the closest he'd do is pat Sherlock on the head.
Sherlock and Mycroft still hold hands
It's very strange to see them arguing over something trivial or over national security while holding hands.
It also doesn't stop people from wondering what else Mycroft has done to Sherlock consensual or not when Sherlock was younger and they wonder if they still do such things.
But of course, they didn't do anything of the sort. Maybe Mycroft used to kiss Sherlock on the forehead but now, the closest he'd do is pat Sherlock on the head.