Why exactly did Walt leave Gray Matter?

The question is answered very well here in an AMC blog posting an interview with the actress who played Gretchen:

Q: What’s it like have Bryan Cranston curse at you?

A: Oh man, he’s a good actor. But it was easy because Vince Gilligan told us exactly what went down between the characters off screen: We were very much in love and we were to get married. And he came home and met my family, and I come from this really successful, wealthy family, and that knocks him on his side. He couldn’t deal with this inferiority he felt — this lack of connection to privilege. It made him terrified, and he literally just left me, and I was devastated. Walt is fighting his way out of going back to that emotional place, so he says, “F— you.” - actress who plays Gretchen AMC blog

Source

The exact reasons surrounding Walter leaving Gray Matter were never covered during show's run. The only in-show information to go on is from the Breaking Bad Wikia page for Grey Matter:

...he [Walter] was dating his female lab assistant, Gretchen ("...and the Bag's in the River"). For reasons not yet explained, Walter suddenly left Gretchen during a vacation with her family, leaving her and his research behind ("Peekaboo").

Further details were then hinted at during the season 5 episode ("Buyout"), when Walter discussed leaving Gray Matter with Jesse. He shares his story about how he sold his stake in the company for $5000 while trying to justify why they shouldn't be selling out their current operation. This scene showcases his embarrassment over leaving his ideas and his creations behind and clearly demonstrates his regret in leaving but doesn't allude further into the details of why.

According to show creator Vince Gilligan and co-showrunner Peter Gould in a new interview with The Huffington Post:

The real reason White left Gray Matter, which serves as part of the motivation for the character’s dark turn, has remained a mystery, but while chatting with The Huffington Post about “Yo Soy Saul,” an original song created for “Better Call Saul,” show creator Vince Gilligan and co-showrunner Peter Gould also finally opened up about one of the biggest unanswered questions from the series:

“Breaking Bad” actress Jessica Hecht, who plays Gretchen, mentioned in an AMC Q&A that Walt left the company and their relationship because he felt inferior. Gilligan confirmed this was true to HuffPost, saying, “She’s correct, and that’s what I explained to her and to [Bryan Cranston] before they shot that big scene between the two of them where they were at the restaurant.”

The scene Gilligan is referring to takes place in the Season 2 episode “Peekaboo.”

“It ends with him being so nasty to her saying, ‘Fuck you,’ and then she leaves tearfully,” said Gilligan. “In my mind, the interesting thing here — and I always kind of hate to nail it down so explicitly — but let’s put it this way, most viewers of ‘Breaking Bad’ assume Gretchen and Elliott are the bad guys, and they assume that Walt got ripped off by them, got ill used by them, and I never actually saw it that way.”

Gilligan explained that the truth is more nuanced. It all stemmed from White’s feeling of inferiority while spending time with Gretchen’s family.

“I think it was kind of situation where he didn’t realize the girl he was about to marry was so very wealthy and came from such a prominent family, and it kind of blew his mind and made him feel inferior and he overreacted. He just kind of checked out. I think there is that whole other side to the story, and it can be gleaned. This isn’t really the CliffsNotes version so much. These facts can be gleaned if you watch some of these scenes really closely enough, and you watch them without too much of an overriding bias toward Walt and against Gretchen and Elliott,” said Gilligan.

Gould added, “I think the interesting thing is not exactly what happened but the fact that Walt hasn’t let it go over all these years. He has no perspective on himself. He gets to the point where all he can really do is try to justify everything that he’s done.”

Walt and Gretchen were an item. Elliot teams up with them to start Gray Matter. Gretchen cheats on Walt with Elliot. Heartbroken and betrayed, Walt leaves Gretchen and Elliott and, in the process, all of Gray Matter.

The show never spelled it out clearly, but there were enough hints to point to what seems an obvious and believable reason as to why Walt left.