Rate of reaction involving different stoichiometric coefficients
My doubt is why rate of reaction is taken as the rate of consumption of N2? 


It's done that way because rates have units, and most people don't pay enough attention to the units.  Usually in chemistry, rates are units of moles per unit time (per unit volume or per unit catalyst mass or per unit surface area or something).  But you need to know moles of what?  

By writing the reaction as $\ce{N2 + 3 H2 &lt;=&gt; 2 NH3}$, you are implicitly defining that a mole of "reaction" corresponds to one mole of $\ce{N2}$, two moles of $\ce{NH3}$, and three moles of $\ce{H2}$.  If you wrote the reaction as $\ce{\frac{1}{2}N2 + \frac{3}{2}H2 &lt;=&gt; NH3}$, then one mole of this new reation would correspond to one mole of $\ce{NH3}$, but only half a mole of $\ce{N2}$, etc.


  Why can't it be the rate of production of NH3? Why can't we say that the rate of reaction is the rate of production of NH3 or half the rate of consumption of N2 or one and half times that of rate of consumption of H2?


It could be any of those things.  The choice is up to you.  You just have to be consistent.  You might this related chem.SE question and answer helpful.  

When you say "the rate", you have to specify what rate you are referring to.  And if you talk about rates "of the reaction", the agreed upon reference is that you are counting moles of species that have stoichiometric coefficients of 1.