Since the p0 is composed of quark-antiquark pairs, it can decay electromagnetically into photons. It requires two photons to conserve momentum
Ok, why 2 and not 1 ?
it is possible, leaving the 2 photons, to make sure that the momentum is not conserved?
Physically, it's impossible.
Why is physically impossible ?
Mathematically, any pair of photons whose sum of four-momentum does not preserve the initial four-momentum satisfies my condition
For example, in the center of mass of the particle that decays the particle velocity is zero, so the 3-momentum is zero and the 4-momentum is p = (Mc, 0, 0, 0) with M the mass of the particle.
If it then decays into two particles we say that these two new momentum are for example (m1c, 0, m1 * 5, 0) and (m2c, m2 * 2, 0, 0), so the first mass particle m1 has speed 5 on the y-axis, the second mass particle m2 has velocity 2 on the x-axis. The sum of these two vectors is ((m1 + m2) c, m2 * 2, m1 * 5, 0) which, as you can see, is very different from our initial p vector.