Some guy on reddit says:
Here's my analysis of her problems in this conversation. Feel free to add.
Ignorance - She didn't understand what the phrase "red tape" means.
Unnecessarily Critical - She bashed you for not distinguishing between government and school.
Animosity - Accusing you of being incapable of a conversaton over one commonly used phrase she didn't know.
Insecurity - She thought you were trying to act smarter than her by using words she wasn't aware of and then making them seem common-sense. This is the primary reason why she wants to cut the conversation short.
Stupidity - Saying that intellectual would be a better fit for your last line when intelligible was the better word.
This also applies across the board.