The reasoning is about the trade-off between decay and risk. Inside three weeks, gamma and color-greek grow quickly while the remaining premium is a small fraction of what was collected, so each additional day earns less and risks more.
It is a heuristic, not a law, and it is worth understanding rather than obeying. The underlying idea — exit when the reward for staying no longer compensates the risk — applies at 30 days in a volatile name and at 10 in a sleepy one.
Example: sell the XYZ 45-day $45 put for $0.90. At 21 days it is worth $0.30, so two-thirds of the profit is banked with a third of the calendar risk remaining. Holding to expiry earns the last $0.30 while carrying the week where a 5% drop costs several dollars.
Related: time-decay-curve, gamma-risk, roll-out, short-premium