Why is there a threshold for pair production?

Due to the law of conservation of energy.

Explanation:

Due to the law of conservation of energy, which states that the total amount of energy in any isolated physical system remains constant over time. Therefore, in pair production the energy of the boson must have higher energy than the sum of the rest mass energies of the created particles, otherwise this process would be creating energy, which violates the law of the conservation of energy.