We fear the intelligence of machines for the same reason for which we assume other animals, such as our dogs, fear us human beings. We put ourselves on the topmost level of all our mental ladders and here, what puts us on a higher step compared to animals is our ability to reason logically and perform complex arithmetics. The intuitive association between "being intelligent" and "doing difficult maths" is what makes us fear the intelligence of machines, since they appear to be so much better than us at that task.
However, I'm wondering if the trite argument of redefining the meaning of intelligence can be of use in this context. If we recognize that intelligence can have different forms, and we take a different type of intelligence, such as the ability to quickly empathise with other living beings, we might see ourselves as equally skilled to our dogs, and perhaps superior to machines. If we take yet another intelligence, for example that of ensuring the biological survival of our species, we even seem to be inferior to most other animals (indeed, the so-called "progress" led us to making less and less children, so much so that the Western society is in demographic recession...).
Yet, somehow, we acknowledge that other animals are "living beings like us" (with different types of intelligence, I add). In other words, we treat other animals agnostically with respect to their intelligence. But why don't we apply the same agnosticism to machines? Why are we afraid of - maybe - finding out that they also are "living beings like us"?
As an old sci-fi adage goes, sufficiently complex technology is indistinguishable from magic and, one might say, from life. Are we really able to hold the position that the difference between the machine and the non-machine (and the living and non-living) is our ability to describe its inner workings? If so, I would argue that our best zoologist is as unable to comprehensively describe the workings of a dog-machine as much as our best computer scientist is unable to comprehensively describe the workings of a smartphone-machine. Our smartphones might already be, to our eyes, as "alive" as our dogs.
So, if we just put our minds at ease, we might acknowledge that the intelligence of machines is indeed intelligence, just one of a different kind. If we prove to be able to do this, we might even look forward to the future and cherish the opportunity for reciprocal intellectual growth that will happen between us humans, the machines and, why not, our dogs.