Ross is famously unlucky in love in Friends - and while his on-again, off-again romance with Rachel takes central stage, he has plenty of other major relationships over the course of the show. Emily is, of course, one of the biggest - and one of the three women that he marries (and divorces!), after a whirlwind romance. Introduced to Ross by Rachel (ironically enough), the two go from an inauspicious first date to a B&B in Vermont, to marriage at breakneck speed - but they were never going to last.
Starting when Ross "accidentally" says Rachel's name at the altar during their wedding, things go rapidly downhill for Ross and Emily. Emily runs out on the wedding reception, then refuses to talk to Ross, and then asks him to never see Rachel again (which he says he will do, and then continues to see her anyway). In the end, it's no surprise they got divorced, and it was clear from the start that they were never going to last.
She's Extremely High Maintenance
Ross isn't particularly laid-back himself, but Emily shows from the start that she struggles to deal with difficult situations or control her emotions, and that's rarely a good sign for a relationship. When the two first meet, Emily has admittedly been having a tough day, but when Ross starts to tell her that Rachel isn't available that night (and he'll be going out with her instead) she snaps at him and is incredibly rude about it. Later, when she sees that her ideal venue for wedding is being torn down, she throws a tantrum and threatens to call the whole wedding off!
They Live In Different Countries
This isn't always a dealbreaker, but it's a pretty difficult thing to get past, especially for someone like Ross, who has to stay in New York because he has a child there (and Carol and Susan aren't willing to move). Emily was only visiting New York, which meant that they just didn't have enough time to get to know each other slowly - perhaps if she had lived there, things could have been different, but this should have just been a holiday romance.
She Was Already Dating Colin
Something that often gets forgotten is that Emily was actually dating someone when she met Ross - an unseen character named Colin. She quickly realizes that she is falling for Ross and ends things, but it's definitely a worrying sign that their first 'magical' weekend together was actually her cheating on her boyfriend with a man she just met. Given that Ross has his own issues with fidelity, this was not a recipe for a solid relationship.
The Friends Hated Emily...
While Ross was besotted with Emily, none of the rest of the gang really liked her - and with good reason. She made a terrible first impression, and then no one had much of a chance to get to know her.
Instead, they just saw Ross falling head over heels with a relative stranger. None of them really supported the wedding, and at the end of the day, it matters that someone's partner gets along with their friends, especially when the friends are as close as Ross and his gang.
...And Ross Didn't Fit In With Emily's Friends, Either
It wasn't just Emily who struggled to fit in with Ross's friends, Ross didn't exactly fit with Emily's friends, either. When he attempted to play rugby with some of her friends, he gets absolutely destroyed, and physically injured - not to mention making a fool out of himself and failing to actually connect. It's hard to see these two in a long relationship that involves spending a lot of time with each other's social circles.
They Didn't Have Much In Common
Perhaps one of the reasons that these two didn't get along with each other's friends is that they didn't seem to actually have anything in common. She's not explored as a character in any real depth in the show, and things like her profession and hobbies are pretty much unknown - but they are definitely not mentioned as similar to Ross's. The few things that fans do learn about her preferences, though, (like her love of Rugby) don't match up with Ross's hobbies at all.
They Moved Way Too Fast
Definitely one of the most obvious red flags was the speed at which their relationship moved. A first date (that wasn't even intended to be a romantic date) became a weekend away together, which became a long-distance relationship and engagement in only a few weeks!
While there's something romantic about a speedy romance, this was so fast it was raising red flags with the other friends, too.
They Were Fighting From The Moment They First Met
While Ross and Emily were occasionally shown being loving toward each other, they spent a worrying amount of their time on-screen fighting. Their first meeting saw Ross unenthusiastic and Emily angry, and they battled about everything from how important the wedding was to Rachel's presence in his life. Fights may be a normal part of a relationship, but this many intense fights in only a few weeks is just too much.
Emily Was Intensely Jealous Of Rachel
Emily having some issues with Rachel does make sense, after Ross said her name at their wedding! However, Emily takes things far too far when she and Ross are talking about patching things up. Asking him to cut someone out of his life is extreme, especially when she is his sister's best friend and roommate. On a practical level, that would make things near-impossible. Then asking him to throw out all the furniture he owned, and literally anything in his apartment that Rachel may have even touched is taking it to a whole new level of unreasonable.
Ross Was In Love With Rachel
The biggest issue, of course, is that Ross has been in love with Rachel since they were teenagers - and no one else was going to compare. The fact that he said Rachel's name at the wedding was proof enough, but it wasn't the only thing that made this obvious. Everyone could see that Ross was still pining over Rachel, and this was just a rebound that should never have become a marriage.