how did gatsby and daisy meet? and why couldn't they be together?

But the scene in the book is funny and prescient the clock is broken to begin with. Gatsby is trying to reverse the progression of time, undoing all that has transpired in the five years since he's seen Daisy, so Fitzgerald subtly reminds us in this scene that time can only move in one direction: forward. In the book, after Gatsby catches the clock, he puts it back on the mantel and apologizes. Nick comments, "I think we all believed for a moment that it had smashed in pieces on the floor." Like Gatsby and Daisy's relationship, the clock is "defunct," no longer ticking, regardless of Gatsby's furious efforts. Though the clock appears intact, as Gatsby and Daisy once again appear in the same place, some hidden mechanism is no longer working.

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Great Gatsby - Gatsby and Daisy

Pretty as a picture: Genevra King, a rich debutante, was the great unrequited love of F. Scott Fitzgerald. Much like the story he would wrote about iconic characters Jay Gatsby and Daisy Buchanan, their relationship was doomed

Gatsby and Daisy by RainingTragedy on DeviantArt

In the beginning of chapter VII we get to know that Gatsby and Daisy have been spending a lot of time together. In order to avoid the gossip about these rendezvous Gatsby fires all his servants and replaced them with new ones. Parties at his house become rarer and it becomes more quiet around his house. During that period Nick is invited to lunch at the Buchanans’. Jordan and Gatsby are present , too and tense conversations between the characters begin. Gatsby and Daisy make Tom jealous by flirting with each other and the provoking situation ends in a trip to New York. Tom challenges Gatsby to change cars to drive to New York and with a short stop at Wilson’s gas station to fill up Gatsby’s yellow car driven by Tom they all meet again in the parlour of a suite in the Plaza Hotel near Central Park. There, Daisy’s real feelings about her past with Gatsby and Tom are conveyed. Gatsby is disappointed about the fact that she loved Tom once ,too and accuses her of being confused and not knowing what she is saying. When Tom starts to argue with Gatsby about what he found out about his real past it gets too much for Daisy and they head on home- this time with Gatsby and Daisy in Gatsby’s car.

Jay Gatsby and Daisy Buchanan : A Long Lost Love. - ThingLink
As the summer progresses, Nick eventually garners an invitation to one of Gatsby’s legendary parties. He encounters Jordan Baker at the party, and they meet Gatsby himself, a surprisingly young man who affects an English accent, has a remarkable smile, and calls everyone “old sport.” Gatsby asks to speak to Jordan alone, and, through Jordan, Nick later learns more about his mysterious neighbor. Gatsby tells Jordan that he knew Daisy in Louisville in 1917 and is deeply in love with her. He spends many nights staring at the green light at the end of her dock, across the bay from his mansion. Gatsby’s extravagant lifestyle and wild parties are simply an attempt to impress Daisy. Gatsby now wants Nick to arrange a reunion between himself and Daisy, but he is afraid that Daisy will refuse to see him if she knows that he still loves her. Nick invites Daisy to have tea at his house, without telling her that Gatsby will also be there. After an initially awkward reunion, Gatsby and Daisy reestablish their connection. Their love rekindled, they begin an affair.Myrtle Wilson dashes out in the road in front of her husband’s gas station as Gatsby and Daisy drive through the valley of ashes. Gatsby’s car hits her. She is killed. The car drives on – it leaves the scene of the accident.
Nick and Jordan and Tom come upon the accident scene. All the gory details of the accident are related. Jordan and Nick then drive on with Tom to the Buchanans’ place.
Thank you BigMurph26 for this Gatsby and Daisy gif:

Gatsby and Daisy- Young and Beautiful

That same night, at the ash-heap halfway between New York City and East Egg, George Wilson has Myrtle locked up in their room, where he plans to keep her until they move west. Myrtle escapes, however, but when she rushes out into the night she gets hit by a "big yellow car" (147) that doesn't stop. On their drive home, Tom, Jordan, and Nick -- who had been behind Gatsby and Daisy -- come upon the crowd gathered outside Wilson's garage. When Tom discovers his mistress has been "instantly killed" (147) he quickly makes the connection that Gatsby's yellow car has killed her.

The Great Gatsby - Gatsby and Daisy's Past

Gatsby and Daisy- Beautiful Girl

As Gatsby and Daisy drive by Wilson's garage, Myrtle runs out to the car. Daisy and Gatsby do not stop. Tom, Jordan, and Nick come on the scene next, and stop to see what is going on. Tom is distraught to learn that Myrtle has been killed, and when George describes the yellow car, he is certain Gatsby has killed her.

Young and beautiful | Gatsby and Daisy

You Will Be In My Heart - Gatsby and Daisy

After making conversation about the terrible heat, and briefly introducing her daughter to the group, Daisy proposes that they all go into town, meaning that they should go to Manhattan. After she makes the suggestion, she exchanges a few words with Gatsby, and Tom, watching the couple, realizes they are having an affair. Tom becomes angry, but hides it by agreeing that they should all go to New York. Gatsby and Daisy drive Tom's car. Tom, Nick, and Jordan take Gatsby's bright yellow car.