Using this definition, can you summarize why hyperventilation is considered dangerous?

Voluntary hyperventilation before beginning voluntary apnea is commonly believed to allow the person involved to safely hold their breath for a longer period. In reality, it will give the impression that one does not need to breathe, while the body is actually experiencing a blood-oxygen level that would normally, and indirectly, invoke a strong dyspnea and eventually involuntary breathing. Some have incorrectly attributed the effect of hyperventilation to increased oxygen in the blood, not realizing that it is actually due to a decrease in CO2 in the blood and lungs. Blood leaving the lungs is normally fully saturated with oxygen, so hyperventilation of normal air cannot increase the amount of oxygen available, as oxygen in blood is the direct factor. Lowering the CO2 concentration increases the pH of the blood, thus increasing the time before blood becomes acidic enough so the respiratory center becomes stimulated, as described above. 
The primary urge to breathe is triggered by rising carbon dioxide (CO2) levels in the bloodstream. Carbon dioxide builds up in the bloodstream when oxygen is metabolized and it needs to be expelled as a waste product. The body detects carbon dioxide levels very accurately and relies on this as the primary trigger to control breathing. Hyperventilation artificially depletes the resting concentration of carbon dioxide causing a low blood carbon dioxide condition called hypocapnia. Hypocapnia reduces the reflexive respiratory drive, allowing the delay of breathing and leaving the diver susceptible to loss of consciousness from hypoxia. For most healthy people, the first sign of low oxygen levels is a greyout or unconsciousness: there is no bodily sensation that warns a diver of an impending blackout.
If a person loses consciousness underwater, there is considerable danger that they will drown. An alert diving partner or nearby lifeguard would be in the best position to rescue such a person. Static apnea blackout occurs at the surface when a motionless diver holds their breath long enough for the circulating oxygen in blood to fall below that required for the brain to maintain consciousness. It involves no pressure changes in the body and is usually performed to enhance breath-hold time. It should never be practiced alone, but under strict safety protocols with a safety guard or equipment beside the diver.

Hyperventilation does not increase the amount of oxygen available but artificially decreases carbon dioxide (CO2) levels in blood and lungs. 
Because the primary urge to breathe is triggered by rising carbon dioxide levels, it gives false impression that one does not need to breath. This can lead to sudden lost of consciousness. If this happens underwater, there is a considerable risk of drowning. 
This is why hyperventilation is considered as dangerous and should be avoided.