I think the sticking point for many people is the definition of intelligence. You'll get people who protest "but it's just doing those things for treats!" or whatnot, but it's the ability to memorize all of those gestures/words that makes it impressive. I think it's kind of similar to the "do submarines swim?" question.
What it really is is a hold-over idea that humans have some innate specialness.
Animals are just doing tricks. Humans who learn to play a sport aren't.
Animals are just doing it for the food. You go to work every day, why?
It's worth noting that this has been an idea that has less evidence to back it up all the time. This idea will eventually be disproven, but in the meantime, there are an awful lot of people emotionally invested in this specialness being true.
