Why does diatomic molecules (such as H2 or O2) have a heat of formation of zero?

Heat of formation of a substance is defined as the energy change when 1 mole of the substance is formed from its constituent elements in their standard states.

The standard states of hydrogen and oxygen are H₂(g) and O₂(g) respectively. Therefore, the heat of formation of H₂(g) or O₂(g) is the energy change of formation of 1 moles of H₂(g) or O₂(g) from 1 moles of H₂(g) or O₂(g) respectively. Obviously, the corresponding heat of formation is zero.
H₂(g) → H₂(g) …. ΔH = heat of formation of H₂(g) = 0
O₂(g) → O₂(g) …. ΔH = heat of formation of O₂(g) = 0

The heats of formation of H₂(g) and O₂(g) are both zero. This is because they are chosen as the standard states of H₂(g) and O₂(g) respectively.

The "heat of formation" is defined as the enthalpy change associated with forming the compound from the elements in their standard states. (The standard state is the way the element is found in nature or a solution at 1 atm of pressure. It refers to the physical state (solid, liquid or gas) or to a 1M solution. The standard states do NOT include a temperature. You can have the standard state over a wide range of temperatures.)

The heat of formation of an element in its standard state is defined as zero. H2 and O2 gases at 1 atm are in their standard state, that is, a diatomic gaseous molecule, since that is the way they are found in nature. Individual oxygen atoms are not in their standard state, and have a nonzero heat of formation.

Heat of formation of O2(g) = 0
Heat of formation of O(g) = +249 kJ/mol ....... notice that the heat of formation of an oxygen atom is positive (endothermic). Energy must be added to break the O=O bonds in O2.

This is a matter of definition. 2H --> H2 is highly exothermic, but H2 is the only useful way to use the element - so we start there. It's like using the Greenwich meridian for longitude or having the day start at midnight.

heat of formation is what happens when you change from the basic substance of reference to another substance. Diatomic molecules (these diatomic molecules at least) do not exist out there as free monatomic elements so we use the diatomic form as the reference form. All elements have a "zero" condition, what we choose to consider as its starting condition when we look at changes.

Something has to be the "zero" condition because we do not measure relative to an absolute energy content, only a change in energy. We cannot measure absolute energy content. We can measure change in energy because that involves addition or subtraction of heat and work. So, we just choose what we want to call "zero".

Zero as we measure and report it does not really mean anything in absolute terms. It is a measure relative to some standard condition.

The heat of formation is the amount of energy required to make the molecule from its base atoms such as water from two hydrogens and an oxygen.
However, both oxygen and hydrogen are naturally found in pairs, and so no additional energy is required to get them to this state.