Now, you may not fully understand the full on hold Eris Discord has on messing with mythological notions and items.
You know of the Original Snub, you know of the many places love has been born and you know of the most famous reindeer of all... you guys are weird by the way. Very very damned weird. There is a lacking of words in all the languages of the world to describe your weirdness.
Before Greek Mythology, there was that Egyption stuff. With Seth, Horus, Maat and what not--however, that is only the localised version to that area. See, overall there was one Mythology at the time, which can be tied together as "Leviant". Spoilers: everybody dies at the end.
What is worse, is there are many items that have counter parts in other later mythologies in the Leviant. We all know that Aphrodite was just kind of born when Zeus happened to initiate a set of events to have a large wang drop into the ocean. Never mind that Aphrodite's birth just happened to be near the exit to a place known as Tartarus. A prison for immortal beings to just chillax. This Aphrodite, a Titan (there are several Aphrodite's running around... even without it having been a popular baby name) was the one present at the original snub... with a golden apple rolling just in.
Jump back to the Leviant, and how the Goddess of Love died. She had a thigh bone and her breast bone pulled from her body--and because doing that totally would not kill anybody, it was fashioned into a spear, to kill her. Stories of this impressive feat continued on--as apparently, she was still hard to kill after having her thigh bone and breast bone ripped from her body. It is like it is an early example of X-Men or something.
This Goddess, upon death, had a tree grow where her heart fell--said to produce Golden Apples ever few hundred years. Eris Discord, having an insane amount of knowledge--and only a vague amount of patience to deal with people, figured she'd have fun here.
See, Eris is more than familiar with how little history books get things correct. She also knows details will be missed in myth and legends. Having access to a Delorian that she would drive around the streets of Ancient Greece (why do you think the Greeks didn't like her that much)? She now was just having fun messing with the history books.
So, upon the snub from the wedding, she figured she'd have some fun. See, as we all know Aphrodite was "born" in the struggle of a Titan being castrated, right next to the entrance of Tartarus... and totally not Astarte just wandering out in the confusion, strife, struggle and discord. Which none of those conditions would allow Eris to have any clue as to what is going on, or be present to observe this little get out of jail free penis.
The official story has her being born there. Any notion of her being imprisoned and coming out of the water closet by help flying junk is just causing trouble. Eris responding to that with the inevitably weird comment about "Being composed of boxes", her misunderstood translation of "I'm Boxxy" in Greek. Eventually the other deities avoided her, for how damned weird she seemed.
So, she took the apple that grew from the site of Astarte's death. Scribbled onto it, "for the prettiest one"--as people just could not handle subtle and Eris was not one to avoid it where possible. Tossing it into the Wedding... it drove the three Goddesses nuts for the now much more obvious reasons.
Aphrodite, being on the lamb--not in the usual welsh notion either--nor in the argonaut fashion--did not want any evidence for people to figure out she kind of high tailed it from Tartarus.
Athena, knowing of a few legends of Golden Apples--having read about them--and somewhat wanting to know the nutritional components of the apple having been made as such. Wanted it, for forensics analysis. True beauty is only worth proper dissection... or something.
Hera saw something shiny, and was scared that it may indicate somebody else cheating on her brother-husband. Hera was one of those deities that existed before Science gave us the Maury Palovic show. Now that we can watch Maury, Hera's existences woefully inadequate and not required at all any more. Besides, we all know that Hera was secretly a man for seven hundred years of her marriage to Zeus--and he was still shocked when he learned it.
Eris caused a war, over how to properly handle evidence... and nobody even figures this out. Hail her great awesome might! Her glory! Her ability to cause trouble!