Zack first meets Aerith in a suspiciously familiar manner-- he crashes through the ceiling of a run-down church within the slums of Midgar onto a patch of flowers. Having believed himself dead, Zack wakes up to someone he mistook as an angel; the girl corrects him and replies that she is merely a girl named Aerith.
After introducing himself as well, Zack attempts to repay her for briefly taking care of him, but Aerith kindly rejects, saying that she really didn't do very much. He persists, and cheerfully offers to take her on a date. Aerith thinks the idea would seem silly, much to Zack's dismay. Before they can carry on their conversation, Aerith stops him from treading on the flowers.
Aerith scolds him for what he almost did, and states that people wouldn't normally step on flowers. Zack tells her that he isn't "normal", hinting at his unique characteristics that make him a SOLDIER.; he doesn't tell her this at that moment, however. Zack carries on, and comments on the rarity of flowers in Midgar, let alone the slums. He then gives her an idea: he suggests that she sell the flowers throughout Midgar, since they don't come around too often. Although he says it would be very profitable, it would also mean that Midgar would potentially be filled with flowers, something that Aerith never really thought of.
Both Zack and Aerith share a characteristic in that they live day to day without bitterness and only reminding themselves about the joy life has the potential to bring.
Zack's bright and cheerful confidence attracts Aerith's attention, and they later become each other's romantic interest.
"The setting that “falling from the roof of the Church” repeats Aerith’s encounter with Cloud was decided in the beginning. Though we’re talking about love, they are still young back then and there’s no time to describe “how they become fond of each other” in the game. So I made it like “falling into a sudden crush"
-- Nojima Kazushige, Crisis Core Ultimania
Zack wakes up in a manner similar to that of Cloud in the original Final Fantasy VII installment; this later points to why Aerith repeatedly finds similarities between him and Zack.
In addition to identity comparisons, Zack's error in calling her an angel, is more than just a cute, superficial comment. In a way, it foreshadows Aerith's transformation into a sort of divine spirit following her death, but it also embodies the kind of person she is-- a kind, beautiful creature who looks after the people she dearly loves. Cheesy descriptions aside, Aerith doesn't necessarily start off this way, but her journey throughout the other Final Fantasy VII compilations is certainly evident of this.
Despite Zack's comment on not being "normal", Aerith is, unbeknownst to him, a Centra. This puts them on the same scale in terms of being different from everyone else. Though they are not quite the same, perhaps Aerith understood him on that particular level-- certain qualities about themselves, though not necessarily obvious, separated them from normal people and the rest of everyday society. At the same time, although Aerith is indeed a powerful Centra, we forget sometimes that she was once a girl who lived an ordinary lifestyle. In the same respect, Zack wasn't always a 1st class SOLDIER either; he was once a kid would lived in an old backwater half-way around the world.