As mentioned in Tyson’s sports headcanon:
Though Tyson was pretty good at rock climbing when he went with his brother, Jethro, to his classes, it wasn’t one that Tyson particularly enjoyed. He prefers the freedom to pick his own paths that climbing trees, mountains, or parkouring around London provides.
He doesn’t find climbing rewarding in the same way as other exercises. He doesn’t mind being at heights and the view can be enjoyable, but the actual task is one that disinterests Tyson.
To take a break - or stop altogether - when he’s running or lifting weights before meeting any significant stopping point doesn’t feel like a defeat, as he has still achieved whatever distance and however many lifts as the point he stops at. Whereas when he’s climbing, Tyson has either completed that attempt at climbing the wall or he hasn’t. It feels like a defeat to lower himself back to the ground without completing the wall.
Parkouring around London goes into the running category for Tyson. It’s like running through an obstacle course in his army days. Every building he manages to get over, around, or through counts as a success.
Even when he needs to haul himself over a ledge or climb up drainpipes to make his way to a window, Tyson would never put that into the same category of climbing up as a rock wall. In his mind, it’s more dynamic and involved than a climbing wall.