I don't see how this is an issue of sexism, at all. That's a major stretch.
It's really not a stretch, although I don't think Bernie meant it in a sexist way. I think he meant it in "I'm a ass, especially when I'm not getting my way." Look, there is no one in their right mind who doesn't think Hillary Freaking Clinton isn't insanely qualified to be President. People may not like her, may not think she's ideologically in line with them, but to say she's not qualified is a lie of epic proportions. There is no one in the modern era who is more qualified than she is. Period. Full stop.
So, when someone makes such an obviously idiotic statement, it's natural to look at what differentiates her from another candidate. If Bernie is saying he's qualified with his paper thin resume, then I think it's a bit natural for people to try and see what's the difference between the two. Gender jumps off the page.
Women are socialized to believe that they have to work twice as hard for half as much. As a society, we internalize that and just go with it. Women are always accused of being "ambitious," like it's unseemly for a woman to have any aims other than what we've collectively decided she should have. Bernie's campaign used the ambition line against her a few days ago.
So, I don't think Bernie meant this in an overly sexist way. But, when you combine a lot of the things his campaign has said over the last few months, reading slight sexism in this particular attack isn't entirely outside the realm of logical interpretation.