I know there is evidence that it is not predetermined and I tried reading articles on it but most of them either don't explain the intuition behind the experiment or they speak in a foreign language (That language being science). If you could explain the intuition behind the experiment and also give an analogy that would be great.
Quantum entanglement can not be described as a predetermined correlation between particle's states because of the observed violations of Bell's inequalities. All of this is best explained in the language of science and math. If you want to avoid such explanations, you might try an explanation like this: quantum casino - less than zero chance. In short: would you want to emulate Bell inequality violations via predetermined correlations, you would need negative probabilities in the preparation of the particle states.
How do we know that photon entanglement isn't the result of the photons's states being predetermined?
Photons are elementary particles, and elementary particles cannot be explained without quantum mechanics.
Quantum mechanics describes the state of the photon and the system it resides in, all in one probability distribution.
It is analogous to throwing a coin heads/tail. There exists a probability distribution for the result of the throw/experiment, it is 50% for each. If you throw heads up, you know the other side is tails, as it is entangled, but the state itself is not known until you throw the coin. It is one point to accumulate in the 50 50 probability distribution.
With particles there exist conservation laws, analogous to the constraint if heads is seen the other side necessarily is tails, but that is all. The experiment itself, the throw, is random . Quntum mechanically the probability is predetermined but not the state the photon will be found, it is a draw in the probability distribution.