There are two main reasons for Churchill's, unusual, shall we say, fighting style in WWII. The first of which was the tactical benefit. Churchill was an accomplished archer, representing Great Britain in the 1939 World Archery Championships in Oslo, ranking 24th of 37 entrants. He was able, therefore, to make good use of a weapon far quieter than a gun. He also made good use of his sword, capturing many Germans at swordpoint - the best example of which was when he 'captured Pigoletti and the entire garrison of forty-two plus a 81 mm mortar and crew'. Wielding a claymore, Churchill made a very intimidating figure. His habit of breaking out the bagpipes, in addition to this, was certainly a boon to the morale of his men.
The second reason, and the one which most likely played a larger part, is that it was just Churchill's personality to do so. Throughout his life, he showed himself to be utterly unafraid, and an avid thrillseeker. He also had a propensity for playing the pipes at every opportunity. His close friend, Rex King-Clark wrote an account of time they spent together travelling to Scotland, France, and Italy. Churchill constantly set 'tasks' for the two men to complete. The first involved swimming through cold waters to a wrecked cargo ship Jack had spotted. King-Clark returned to shore after they made it to the bridge, though Churchill went about exploring the cabins, before returning to shore and, still naked from his swim, took up the pipes. Later on their trip to Italy, Churchill played his pipes at the crater of Vesuvius. King-Clark tells the tale far better than I can:
'Jack, meanwhile, doodle-sack under arm, had a more ambitious objective in mind; he was determined to climb the central cone of ash — the 'boiler house chimney' of the volcano. No guide would go with us, however, until, finally, we discovered a boy asleep on a warm slab of lava, who on being awakened by Dina and Marisa (he must have thought he had died in his sleep and arisen in some angelic heaven) and being shown a handful of lire, volunteered to take us up. So, leaving the girls behind, we scrambled up the steep side of the cone, the hard, jagged lumps of ash sliding away beneath our feet, the crepe rubber soles of my shoes melting beneath me, until we stood on the lip itself, looking down on the swirling, bottomless pit of smoke and steam. At intervals, there would be a quiet rumble and hiss, and suddenly, out of the steam, an accumulation of stones and debris would shoot straight up to 50 feet or more before dropping back into the pit. When this happened, the boy and I would cower back, hunching our head and shoulders protectively. To me, it felt eerie, primeval - beyond man's control. To Jack, however, it was glorious drama. He stood there, his Macmillan kilt bright against the grey smoke, chin up, fingers working, left elbow rhythmically squeezing the sack, right foot tapping the beat - playing a wild, heathen dance to Vulcan, the Roman firegod.'
Churchill certainly had a taste for the theatrical, and was comfortable being the centre of attention. During the trip through Europe, King-Clark mentions several occasions on which the two kilt-clad men made a spectacle of themselves, Churchill playing the pipes with King-Clark dancing the Highland Fling. Further evidence of his habit to put on a show is from after he received a wound capturing Maaloy Island: 'His 'wound' healed quickly - too quickly, in fact. "I had to touch it up from time to time with Rosamund's
Churchill is also known for surprising train passengers in his later life, when he would throw his briefcase out the train window into his back garden so he wouldn't have to carry it home from the station.
Finally, there is an argument that it is just honestly how he thought a soldier should behave. He is often quoted 'Any officer who goes into action without his sword is improperly dressed.', however I feel a more fitting testament to this aspect of his character is what King-Clark wrote about Churchill's experience of the Dunkirk campaign:
'...he was, I know, genuinely surprised and disappointed to discover that all men were not as fearless as he. Perhaps Jack never fully appreciated the earnest desire of the average soldier to live to fight another day, or that the 'squaddie' follows most happily the leader who respects, within the scope of events, this basic sentiment.'