Why Fall-arrest lanyards must be attached to something that can withstand the shock load of an arrested fall, and on a tower that is the main vertical legs, which carry the structural load and are continuous from top to bottom. Rungs, cross braces, guy brackets and the mast are secondary members sized for much lighter loads and can bend, shear or pull loose. Standard tower climbing safety practice, and OSHA-style fall protection guidance, is to keep the lanyard around a tower leg at all times while moving.
Watch out Tower rungs are tempting because that is what you are grabbing and standing on, but step bolts and cross members are only meant to hold your body weight in a static way, not the sudden force of a fall.
Clip to the legs, not to what you step on. Legs carry the tower, so let them carry you.