Why does a person sitting in one train think that the other train is at rest when both the trains are moving on parallel tracks with the same speed and in the same direction?

This happens due to the relative nature of velocity. The relative velocity of the train with respect to another train felt by the person is the difference in the velocities of the two trains.

\[\text{i.e.}\;\;v_{\text{rel}}=v_{\text{train}}-v_{\text{person}}\]

Since both the trains are moving with a same speed, $v_{\text{train}}=v_{\text{person}}$.

\[\therefore v_{\text{rel}}=0\]

So, the person sitting in one train thinks that the other train is at rest.

[Read: Motion in a Straight Line]