Why is the standard enthalpy of formation of elements in their native forms zero?
It is purely a matter of definition. A standard enthalpy of formation describes the change in enthalpy during the formation of 1 mol of a target compound by reacting the (pure) elements it consists of, whereby each element is expected to be in its most stable modification for the given temperature. Now take the case of oxygen as an example: At standard conditions $\ce{O2(g)}$ is the most stable modification of oxygen. That means at standard conditions the reaction

$$\ce{2O &lt;=&gt;&gt; O2(g)}$$

is defined in such a way that each of the elemental $\ce{O}$s are defined to be exactly the same state as an oxygen atom that is part of an $\ce{O2(g)}$, i.e. their enthalpy $2H^{\circ}(\ce{O})$ matches exactly that of $\ce{O2(g)}$: $H^{\circ}(\ce{O}) = \frac{1}{2}H^{\circ}(\ce{O2(g)})$. This gives you a reference point for $H^{\circ}(\ce{O})$ which is otherwise nearly impossible to measure much as the Standard Hydrogen Electrode is used to set up a reference system for the electrode potential.

A table showing some standard enthalpies of formation can be found here. There it is also indicated which phases are used as reference form.