Here's another way to look at it.
You have 1 LED on, with Vf of 2V, with 220 ohm resistor current flow is
(5V - 2V)/220 = 13.6mA, and 3V across the resistor.
Now you turn on another LED - say the same Vf of 2V. The current flow thru the resistor cannot increase - 3V/220 is still 13.6mA, now shared among 2 LEDs, so brightness will suffer. Add a third LED - now 13.6mA is shared among 3 LEDs.
Hence the need for a resistor per LED.