Lost Chrono Trigger Subplot Deemed Too Depressing

Square's Chrono Trigger stands out as one of the best RPGs from the Super NES era of gaming and would later go on to spawn a semi-sequel in Radical Dreamers, an actual sequel for the Sony PlayStation, and enhanced remakes for both the PS1 and the Nintendo DS as well as mobile platforms. The story of how a band of unlikely heroes band together via time travel to destroy an ancient space parasite eager to devour the planet is one of gaming's most detailed, most surprising tales, and while the game offers plenty to do and many sidequests to explore, one subplot was dropped from the game during development because it was deemed too depressing. In a game where time and fate regularly screw with the protagonists, how depressing did a story element have to be in order to be scrapped?