[drostie]

Because the timescales that you're "moving" on are very long from a relativistic perspective. If we localize you in spacetime you're maybe a meter long in one direction, two meters in another, half a meter in a third, and... 30,000 km in the fourth. If we look at you on the nanosecond timescale that you need to see time as "meters" we find that except for, say, electrons' worldlines about the nuclei, your worldlines are very much all parallel to each other.