Fortunately, it doesn't happen too often, but sometimes some people know your weak spots and play upon those weak spots to get you upset.
How do they do this?
This can be done via a look, lack of response, certain words, or public/private challenges.
I usually get caught unaware at these moments and have become upset. I always go back to the worst time it happened when I got very upset at a meeting and was harshly punished for getting upset. Looking back at that event, as I have done over and over again, I realize that the "poking" had been going on for a long time, and I let it go each time unaware that it was building within me. I should have been outspoken about the troubling events leading up to my getting upset as they were happening, and I should have been cognizant that I was probably being baited in some ways.
It's important to be mindful of those who seek to "poke" your weak spots, and have a plan as to how to deal with those kinds of people.
What can a teacher do?
First, listen carefully to understand the situation well. Write down what is said to reflect on later.
Next, don't commit, respond, or question right away. Give yourself time to consider the information carefully so you understand exactly what is being said or requested and why.
After that, in time, be ready to write clarifying questions that restate words spoken and request greater clarification with respect and honest interest. It's good to write this out as then you'll have a record of the information to refer to.
See the issues for what they are--most issues that "poke" us are small in nature, and more annoying than consequential. Further, seeking the help of allies in situations like this can help too.
Finally make sure that your efforts in the matter at hand are well-directed too. Remember it's okay to go "hard on the problem, but not the people."