While enjoying and learning from Danny Schoemann's answer, I'd like to offer another route to understanding the idea that Ben Zoma went insane.
In describing the episode, the Talmud identifies the effect of Ben Zoma's experience in entering pardes with a particular biblical verse:
בן זומא הציץ ונפגע ועליו הכתוב אומר (משלי כה, טז) דבש מצאת אכול דייך פן תשבענו והקאתו
Ben Zoma glimpsed and was harmed. And with regard to him the verse states: “Have you found honey? Eat as much as is sufficient for you, lest you become full from it and vomit it” (Proverbs 25:16).
Although this is the only information given on Ben Zoma's experience, it is instructive. Rambam, misattributing the verse to Elisha ben Avuya (Aher), elaborates on the verse's allegory of sweet food to the nature of knowledge:
Though great, excellent, noble and perfect, it is injurious if not kept within bounds or not guarded properly; it is like honey which gives nourishment and is pleasant, when eaten in moderation, but is totally thrown away when eaten immoderately. ... Let thy mind only attempt things which are within human perception; for the study of things which lie beyond man's comprehension is extremely injurious. (Guide for the Perplexed, ch. 32)
The verse thus gives us an image for one possible outcome after entering pardes, that of the mind expelling what it initially received. This is why Rashi notes that Ben Zoma נטרפה דעתו . Although often translated as "lost his mind" or "went insane" (and Danny Schoemann writes "his mind was jumbled"), the phrase can also be translated, "his mind was devoured."
This understanding of Rashi would fit with Maimonides's explanation of the verse, suggesting that esoteric Torah can have an adverse effect: rather knowledge entering and filling the mind, it alternatively is responsible for the mind's harm; expelling from, or consuming, the mind. Both forms of violent food imagery suggest a person losing their knowledge, a state expectedly categorized in terms of insanity.
On a final note, it should be noted that the question of Ben Zoma's state after the pardes experience is challenging, not only because of the ambiguous terminology surrounding the discussion, but also because there are alternate accounts of the very episode in rabbinic literature. The Talmud Yerushalmi (Hagiga 2:4), for example, notes that it was Ben Azzai who was injured and Ben Zoma who died following the episode. Likewise, it may be that Rambam's version of the Talmud had a slightly different account, thereby assigning the honey verse to Aher.