word for when you let something bad happen just to prove a point

One way to say that would be

You're cutting off your nose to spite your face.

This is a very common idiom, and well understood in all registers.

https://bulletproofmusician.com/productive-failure-how-strategic-failure-in-the-short-term-can-lead-to-greater-success-and-learning-down-the-road/

“Productive Failure”: A Teaching Method Which Leads to Short Term Failure, but Long Term Success

"That organization could be said to be engaged in a productive failure objective."

After reading your question and associated comments several times, I conclude one of the words you're looking for is something like vindictive or a synonym, such as spiteful. From Cambridge:

vindictive: having or showing a wish to harm someone because you think that they harmed you

spiteful: wanting to annoy, upset, or hurt another person, especially in a small way, because you feel angry towards them

Your example sentences with vindictive:

Anyone know the word you would use when you let something bad happen just to prove a point? "You're being vindictive."

The word I'm looking for would be when an organization knows something bad could happen but allows it to prove a point or to teach a lesson. That organization could be said to be vindictive.

In one of your comments, your state:

I need the word to use in this situation: one person wants to let a computer crash so that the user learns a lesson. My response would be something like "We can't be ______, we need to educate them ahead of time..."

The intent here is clearly for the user to learn a lesson not for educational purposes but for punishment purposes. Perhaps this one person is angry with users for some reason, angry with a management decision, or frustrated by a perceived lack of resources -- only you would know their motivation. In any event, they seem to have an urge to punish, in which case you would fill in the blank with vindictive or a synonym thereof, e.g., spiteful.

I can't stop there. I understand that you might not want to use vindictive (or spiteful, etc.) in the sentence in which you reference one person. So, given that your question calls out terms such as proactive and reactive, you seem to be looking for something in between. One possibility is hands off. Again from Cambridge:

hands off: Someone who has a hands-off way of organizing or dealing with something allows other people to make decisions about how things should be done and avoids becoming directly involved

In this case, the sentence re one person would read:

"We can't be hands off, we need to educate them ahead of time..."

Based on the negative context of vindictiveness, I would probably say something like this:

We can't be knowingly (or intentionally) hands off.

A good single word for being knowingly (or intentionally) hands off when you should be hands on is negligent, as suggested by @lux in a comment about two years ago. From Cambridge:

negligent: not being careful or giving enough attention to people or things that are your responsibility:

"We can't be negligent, we need to educate them ahead of time..."