According to Hubble's law, as things move further and further away from one another, there might come a point when their speed gets faster than the speed of light. So, why is it that the speed of light is considered to be the fastest?
The recession rates relevant to Hubble's law are not relative velocities, so there's no reason to compare them to the speed of light.
They can be defined as follows. Conceptually, imagine a chain of galaxies that leads to some target galaxy. Each galaxy along the chain has some small velocity relative to the galaxy before it. If you add all of those relative velocities together, that should give you the velocity of the target galaxy, right? However, velocities in relativity add in a special way; see the relativistic velocity addition formula. The cosmological recession rate is computed by instead just adding the relative velocities naively, without properly using relativistic velocity addition. That's why we should not be concerned that it can exceed the speed of light.
It's also worth noting that the relative velocity between cosmologically distant objects doesn't even have a unique meaning. You can just as well say that it is very high or that it is zero.
(Some text was adapted from one of my answers on Physics.SE.)
I'm standing next to Usain Bolt, he runs off in the opposite direction to the Earth's rotation, why is he consider the fastest human when I'm moving faster than him? Also there are people in planes or spaceships that move faster than him. But that's only from specifically picking frames of reference that make Usain the slowest person.
Same logic goes for these distant objects they aren't moving as fast as they appear, but it's space itself that is stretching and the source of most of the movement. Two bits of space close together hardly moved apart at all but it adds up over large distances. Given the very definition of speed depends on how much space you traverse in a give time, attributing a speed to space itself doesn't make a lot of sense.