From a story perspective, Nate is Andy’s inner voice. It’s completely ok to expect your partner to “make time” for you on your birthday - the rules don’t change just because the “busy” person is a woman. It wasn’t so much that Andy had a job that could launch her career that bothered Nate. It was the way she superficially changed for the job instead of genuinely enjoying it. She didn’t start appreciating fashion or growing a passion for writing about it. She just became obsessed with impressing Miranda no matter how unreasonable her ask and then getting upset with herself when she couldn’t deliver. That’s a kind of gaslighting by an abusive boss and when you start buying into that narrative, as Andy was, you develop an unjustified Imposter Syndrome which can be so detrimental for your career. That’s what Nate and Andy’s dad and her friends were warning her about and a good partner would point this out. And I didn’t think Andy went so far as to actually screw over Emily as Miranda points out in the end - but she does seem willing to ignore impact of her actions on others as Miranda usually does - that’s why Andy needed to quit.