The two most bizarre relationships in the entire game are with Emily and Josh, and I don't think that is a coincidence. Other posters have floated this, but I wanted to unpack it a little.
There are many indications that Emily is struggling with severe substance abuse issues. She demonstrates many obsessive and addictive behaviors. Her relationship with MC is not the only one that is suffering as a result. Her friends are embarrassed to be seen with her, cutting her out of pictures on social media. If you invite her to the homecoming dance she completely self-destructs, and if you don't then you find her crumpled on the steps next to two other characters who are high as a kite. The second time you hook up with her, if you choose to do so, her entire demeanor screams that she is using. She turns her mud wrestling match with Aubrey into a coked-out brawl, actually hurting her. When she ultimately and inevitably breaks things off with MC she does it like a drug deal, meeting him on a park bench in the middle of the night. The guy she cheated with pre-game plied her with alcohol and perhaps drugs to get her to do so, and since the break up it seems that she has continued using to cope with it. Her behavior during the Eurotrip is extremely sad. She doesn't participate in activities and the few times you speak to her she is either laconic or completely incoherent. It is likely that she is spending most if not all of the trip holed up with Josh doing drugs.
Josh is a Russian nesting doll of suspicious behaviors. His signature move for getting with girls is plying them with alcohol and drugs. He is perhaps the only character in the game that actively tries to get you killed, dragging you to a drug deal and pissing off the buyers. Putting that aside he also only prominently appears at the homecoming dance when Emily is your date, and he also doesn't seem that happy about it. He works really hard to hook you up with Aubrey and Amber, basically throwing them at your crotch vagina-first. Not to say anything bad about either lady, but they are pretty easy and indiscreet. At the first frat party he chats up Aubrey the whole night and at the second frat party Emily is chatting with her all night. It is a reasonable assumption that he made this introduction, hoping that Aubrey would let something slip because of her total lack of shame. Right after Emily breaks up with you he drags you to a bar to hook you up with a barfly and then disappears. In fact, he is always disappearing. For some reason, he goes on the Europe trip and is as suspiciously absent from activities as Emily is. Josh may not be a master of manipulation, but he does seem particularly invested in keeping Emily and MC apart.
My take is that Emily doesn't want to break up with the MC. She is completely miserable about it, but - as her supplier - Josh threatened to cut her off if she didn't, and when you are in that deep your dealer is basically the only friend you have left. Maybe Josh loves Emily, but more likely they both just love drugs. Emily's story is perhaps the saddest in the game, and that's why so many players are unsatisfied with it. But all indications are that her story is going to get worse before it gets better. She may have not hit rock bottom yet, but she is headed there pretty quickly.
I'm probably missing even more connections that link Josh to Emily's puzzling story arc, and it is also possible that he has his fingers in a couple of other pies. While the MC is worrying about Charli undermining his relationships Josh may have been doing it much longer. One thing is for certain and that is that Josh is a shitty friend. Emily is a pretty shitty girlfriend as well. They probably deserve each other. Your mileage may vary.