Why can't I mix and match LEDs wired in parallel?

Yesterday I wired up four LEDs to a 3v battery in parallel—orange, blue, orange, blue—but only the orange ones light up. I did test all the batteries beforehand, so I know they all work.

After doing a little research, I have confirmed that these LEDs are, unfortunately, behaving predictably. Instructables says, ”[Wiring in parallel] only works if all the LEDs you are using have exactly the same power specifications. Do NOT mix and match different types/colors of LEDs when wiring in parallel.”

So now I know that it doesn’t work. I’d like to understand why that doesn’t work and if there’s any way I can make it work—say, with resistors?