LONDON—The most tightly wound club in global soccer was running around in the rain on Tuesday night, desperate to avoid a catastrophic act of self-sabotage. In a Champions League semifinal, in front of its own fans, Arsenal could hardly keep the ball. Some 60,000 people inside Emirates Stadium all lived in fear of whichever terrible thing might happen next. It would have been perfectly in character for Arsenal. Despite being one of the richest, most ambitious clubs in the world, its recent history has been defined by near misses and late-season heartbreak—months spent in first place that gave way to…