How might you feel if it danwed on you that the entire culture seemed to wish that the phrase "Chag Sameach" never be uttered again?
I'd feel that I might be feeling a wee bit paranoid and prone to exaggeration.
Your mileage may vary.
We only say Chag Sameach when we see each other in shul or others in our community. We don't run around greeting everyone with it.
Why would I wish non-Jews Chag Sameach (a happy holiday) on Succot if they aren't Jewish? That's just dumb.