She had to try to weasel herself out of an accusation that she broke the rules - a weaseling they didn't buy. So, there was some infraction already extant for which they came.
The charges were "stole knowledge above her age and station" and "practicing the darkest magics". That's
super vague. They don't say she summoned a demon, or hurt anyone (or to what degree), or used it to enrich herself at the expense of others, or anything like that. Here's how I see this going down:
The coven has some sort of system for providing access to magical knowledge based on seniority. Presumably there are dual reasons for doing so – both to make sure you have the requisite skills to actually make use of the knowledge, and also the emotional maturity to be ready for such power. Young Agatha is probably exceptionally talented, and breezed through the earlier lessons, and she's arrogant and wants more. She gets her hands on a book she's not meant to have, and reads it and gains access to its magic. Likely, she has the skills to use the magic ("the rules bent to my power"), but not the wisdom to control it and to know
when to use it. There's probably some sort of incident where something minorly bad happens because of it, alerting the coven to the problem. The coven goes "Nope, last time a baby witch read the Necronomicon we had Pompeji, so let's nip this in its bud", which leads to the attempted murder we see on screen. Note that Agatha begs them to train her to control "it", and she tells her mother that she can be good, but they evidently decide she's too big a threat.
I definitely see the parallels to Wanda here: Wanda tried using her magic to protect her allies from a bomb and throw it away, but didn't account for the fact that she instead put other people in harm's way leading to their death. Had she had more training, perhaps we'd never have the Sokovia accords.