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Why is there a fee for entering and exiting from the same station? How does it work? Is there some way I enter and exit from the same station for free?

The Taipei Metro’s regulations on duration of stays within the paid areas are designed to discourage loitering in stations or trains, homeless persons remaining within the Taipei Metro premises, or express delivery services using the Taipei Metro for deliveries, which may compromise passenger flow and safety.
The Taipei Metro therefore bulletins the "Regulations for use of the Taipei Metro System" by the ticketing machines, of which Item 13 stipulates that, unless due to causes attributable to the TRTC, the duration ticket-holders may remain within paid areas are:
(1) No longer than two hours if entering and leaving from different stations;
(2) No longer than 15 minutes if entering and leaving from the same station.
In addition to paying the original fare, persons in breach of the above regulations are subject to an extra charge equivalent to the minimum single-journey fare promulgated. This charge should be paid at the information counter or will be automatically deducted from the passenger's EasyCard when exiting the station. In accordance with Item 14, passengers who enter and exit from the same station should pay the minimum single-journey fare promulgated. Under certain circumstances, e.g. use of restrooms situated in a paid area, or passengers exiting the paid area immediately after entering (without traveling on trains), station staff may be contacted for assistance.