Because their irides are dilated and the light flash illuminates their retina inside their eyes, which is red by virtue of being well supplied with blood and having no pigmentation.

@ragingloli is correct. It’s why “red eye reduction” is nothing more than a pre-flash before the picture is taken so your pupils constrict.

The closer the flash is to the axis of the lens, the greater the effect. That’s why pro photos use off camera flash with a bracket or light stand. Prepulse flash can reduce the effect, but often makes the subject squint or blink.

Move the tube away from the lens and watch it go away. I use a ring flash circling the lens at times just to induce the effect.