the boy who became the legacy
Zack and Cloud met on a mission.They quickly became close because they both grew up in small villages. I think Cloud reminded Zack of himself, a small country boy who was thrust into a huge city in the hopes of becoming a hero. Zack became a mentor to Cloud, though not as formally as Angeal mentored Zack. Zack always went out of his way to give Cloud tips that would help him improve. Zack even made sure to get Cloud a spot in the Nibelheim mission so that Cloud could visit his family. Visiting his family was something I think Zack always wanted to do again, but was never able to because his constant missions never led him there.
Unfortunately, I think Zack's plan backfired since it ended with both him and Cloud in a world of trouble. The Nibelheim Incident (which would have occurred regardless of Cloud's presence) led to the death of Cloud's family and the capture of both Cloud and Zack as experiments for Hojo. When they got out four years later, Cloud had mako poisoning and could hardly move. Zack was the one who took care of Cloud for an entire year like that, before he died protecting Cloud.
I think that Zack always felt guilty for drawing Cloud into the Nibelheim mission. If it weren't for Zack, Cloud would have lived to move up in the ranks and maybe even become a member of SOLDIER one day. Zack essentially had taken away five years of Cloud's life. On top of that, Zack had failed protect Cloud from Shinra completely. Cloud also felt guilty for Zack. Cloud felt that if he had been stronger Zack wouldn't have died. Which may be true, however, there was no guarantee that Shinra wouldn't have eventually caught up anyway. On top of that Cloud forgot Zack and took on his persona. Despite their guilt I think their bond was incredibly strong, which is partially because they went through similar situations. In the end, I think Zack entrusted his "legacy" to Cloud was because they had become so close during their time together.
Everything about Zack and Cloud's lives are parallel. They came from small villages, left their homes to join SOLDIER, fought Sephiroth, saved the world, dated Aerith, etc. The simple explanation for their similarities is that Cloud had mixed up his memories with Zack's. However, I don't think that explanation accurately describes several of their similarities before that point. I think the reason why they parallel each other so well is because Zack was created for the sole purpose to be a parallel for Cloud.