Two things,

First. I was set off by the complete lack of evidence for the sexism case. The setting that assert sexism is in play is limited to:

  [...] and she continued: “Right, well, it’s because you’re
  young and female.”

And that's it, from there on, the author says It was because of sexism, because her coach said so.

Second. Although the storyline is not a convincing anecdote, it still has value. It is interesting to see that:

  * It's not necessarily people higher in your company that will prevent a women from
  getting promoted.
  * It's not necessarily that women won't get hired for a higher position.
  * If it seems the problem of sexism is solved for many, older individuals still form a
  majority in the senior/execs layers, and their older generation may have sexist ways.

Although the story was not strong enough to make an convincing example, the idea is still plausible and motivates a new way to look at it.