Answer:
Notice he doesn’t say “great minds”, or “geniuses” or “intelligent people”. He’s not talking about IQ or processing power. He’s not saying that smart scientists or philosophers like himself are always attacked by the unintelligent. He says “great spirits”, and a man of that caliber usually chooses his words quite carefully. He’s talking about spirit.
Spirit is not of this world. It is not concerned with the same functions or subjects as the mind. I would say it is rooted/connected to something much deeper, within.
Mind is often opposed to Spirit, because mind seeks to control. Spirit is something different, it can relate to a certain quality of intelligence perhaps, but I’d put it more on the levels of energy, courage, truth and justice. Spirit knows, it can operate with the mind’s help, but it doesn’t even have to ask questions or perform any experiments in our physical space to know certain truths.
When the rare man comes along who embodies those virtues and who acts from Spirit, society - even some of the “great minds” of the time - tend to beat him down, and often kill him. Look at MLK, Gandhi, John Lennon, JFK, the American founding fathers (who had to go to war for their ideas & beliefs, and many of whom were killed), Copernicus, Jesus, Socrates, there are many examples. The physical world is a place of logic and self-preservation, which are often at odds with truth and justice, sadly.