Because the mathematics of relativistic acceleration leads to ever increasing space and time dilation. And whatever formula you look at, it turns out that the velocity is asymptotic to c. People often talk about it requiring infinite energy, which is fair enough, but even if you just consider constant acceleration from the POV of the traveler, the space and time dilation are such that they never reach c with respect to some arbitrary frame.

Essentially, the faster the traveler goes wrt an inertial frame, the more that the time and distance of that frame contract according to the traveler. So for example, when they travel between locations that they naively expected to be a certain distance apart, when they actually pass them, the distance appears to be much shorter (to the traveler).

It is kind of like, as they go faster and faster (wrt a frame), more and more of the acceleration goes into bending space and time, and less and less of the acceleration increases their actual velocity. As a mathematical analogy, it is rather like trying to reach 1 by adding up a finite number of terms in the series 1/2 + 1/4 + 1/8 ...