Cross training

How do we feel about this? I've seen lots of youtube videos about toxic gyms that claim if your teacher discourages cross training, then that is indicative of it being a toxic gym. I have seen a couple reviews of my gym that i train at where people mention my teacher strongly discouraging it as if it is a bad thing.

Personally, while my teacher IS in fact a pretty toxic person, i actually agree with his stance on this. I guess the question i am trying to ask is not how do we feel about it, but more specifically what is the purpose of cross training? I am not talking about going to a school that teaches a completely different art, but why what is the purpose of being at, let's say, a BJJ gym and cross training at another one?

I understand i probably should have posted this in the BJJ sub, given that i mentioned BJJ specifically, but you could really apply this question to any art.