You are tending to confuse the physical concept of time, which is the fourth dimension of space-time, and the human experience of time, which is the accumulation of events.
Though related, they are not the same. Time in the physical sense, is just a dimension like length, width, and height. These are all inter-related, and as Einstein showed with his theory of relativity, they depend on your point of view (i.e. are relative).
Time moves more slowly for objects in motion, but ONLY to other objects. To the object itself, time continues to move normally. Distance shrinks as an object moves faster, but ONLY to the object itself. To other objects, the distance remains the same.
Humans experience time as the accumulation of events, in a linear fashion. X happened before Y, so X happened earlier in time. This is not necessarily true in the physical sense of time, simply because physical time is relative. Human time is strictly linear.
So humans experience the "passing" of time as being the rate at which events accumulate. And human time, too, is variable, as anyone who has spent a year sitting through a one-hour physics lecture can attest.