How/why does hyperventilation sometimes lead to syncope?

Carbon dioxide. This is the main "driver" for us to breathe. Co2 levels in the brain cause the respiratory center to signal breathing. When you hyperventilate you blow off a lot of co2 and the brain senses no need to breathe. Another driver is oxygen but since your o2 levels be high, the brain senses you have enough o2.
Hyperventilation. Hyperventilation causes your body to eliminate the amount of carbon dioxide, which is a powerful vasoconstrictor. By causing vasoconstriction you reduce blood flow and oxygen delivery which can lead to fainting or syncope.
See below. Welcome hypervent can cause alkalosis of the body mess up acid base can cause you to faint.