Angels and demons come from the ethereal realm, a plane of pure energy. The former is made up of pure ether while the latter is made up of a corrupted version. These forces naturally repel each other, like two magnets being pushed together or mixing oil and water. For this reason, it is impossible for angels and demons to interbreed.
However, a solution exists in the form of humanity. A human soul is a tabula rasa of sorts, a blank slate that is free of angelic or demonic energy. Using the soul as a base allows both energies to exist in equilibrium, balancing each other out. This allows both forms to combine properly and amplify each other's effects, making the resulting individual potentially stronger than their parent races. Through an immaculate conception, a human was born on earth with this duality, who is being poached by both sides to join them and their interests.
Why would combining two substances that wouldn't mix in nature amplify each other?