Water is H2O: Two parts hydrogen one part oxygen. Oxygen is flammable; hydrogen is flammable. Why isn't water flammable?

This question is pretty much the same as another one. So, rather than typing a whole other answer, I am just going to refer you to the other question.
http://www.answerbag.com/question_water-extinguish-fire-water-hydrogen-oxygen-gases-helps-fire-burn_77760/

Because Water is the "ash" of the combustion of Hydrogen and Oxygen. When you "burn" Hydrogen in air (or pure Oxygen), you get water vapor as a result.

my sister the college studet says it's because the two fuse together neutralizing the combustion reaction

Hydrogen and Oxygen are flammable because the valence electrons aren't filled, and they are always willing to react with something to catch on fire. The 8 valence electron shell of water is filled, so it doesn't react as much.

Technically, oxygen is not flammable - oxygen supports combustion, not combusts. Oxygen will not burn in air, unlike hydrogen.

A lot of chemistry is balance. The safe place is the middle. Acids and alkalis are both harmful, but cancel out to make neutral salts. Oxygen is strongly oxidising (unsurprisingly) and hydrogen is strongly reducing, which is the opposite property. Together they combine to make water, the substance we use to define neutrality.

Because water is essentially the ash from a hydrogen-oxygen reaction.