So, teaching anything is certainly advocacy in the literal sense. Your math teacher is an advocate for you learning math, and the importance of math. I wouldn't say that's political advocacy, because most people would agree that the rules and facts around of algebra generally aren't something that's commonly debated by governments.
That said, if I was taking a world history class, and my teacher spent the whole class for a year exclusively going over US war atrocities and rights abuses, I think you could argue that would be political, even if it was all factual and correct. They chose to present a set of facts that leads people towards a specific ideology and worldview that influences how they observe politics and the government.
Telling people truths can still be political. Having a popup at work, or a chat message, that informed me of a political candidate's policy positions would be "telling people facts about reality they should know", but is definitely political advocacy. Just because that candidate happens to be in favor of workers rights, or union power, or parental leave, doesn't mean that it's now a relevant work topic.
In a perfect world, everyone would know all their rights and all the laws that are relevant to them, but most people don't. Trying to impose that I take time at work to inform myself about them is thus innately political advocacy. That's not to say that it's a bad thing - I appreciate folks who remind people to vote/registration deadlines, or post informative information about relevant local laws, but it doesn't mean it's not political advocacy to do so when you're doing it in a targeted manner.
It's possible to both think that what this person did was political activism, and to believe that it probably shouldn't have been punished this hard.