There is some element of truth to what they said, though. Not to take away from these other examples, but it is more than seeing new nuances, as in, it can become an entirely new paradigm of thinking. In English, things feel very limited and strict, and your expressiveness (so I find, at least) has an upper limit. With something like Latin, you can express more, with less, and in completely new ways that you would not think about at all in English.
There is more to this argument, but this is a good start, I think.
There is more to this argument, but this is a good start, I think.