Stoichiometry and POAC Contradiction

Lets say we have the reaction 


$$\ce{H2 + O2 -> H2O}$$


And we are given 10 moles of $\ce{O2}$ and are asked that 
How many moles of hydrogen gas do we need to complete the reaction ? 


Stoichiometry gives the answer as 10 moles but by applying Principle Of Atom Conservation, we get 


$$\text{Moles of }\ce{H2} =2\cdot\text{moles of }\ce{O2}$$


Why is the POAC giving wrong results? 




You applied the POAC incorrectly . Even your stoichiometric answer is incorrect.


First Balance the reaction 


$$\ce{2H2 + O2 -> 2H2O}$$


We get that one mole of $\ce{O2}$ requires 2 moles of $\ce{H2}$.
Thus 10 moles $\ce{O2}$ need 20 moles of $\ce{H2}$.


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