Why are general relativity and quantum mechanics incompatible?

Both theories work very well in their respective domains of influence. However, certain regions in the universe, such as the center of a black hole or the very early universe (at the Big Bang), suggest properties that are both heavy (where general relativity is useful) and small (where quantum mechanics is useful). Both theories have to be unified; however, it is very difficult to unify these theories because

(1) Their underlying philosophies are different; whereas general relativity is deterministic, quantum mechanics is probabilistic, and hence each theory uses different mathematics.

(2) General relativity describes space time as smooth and malleable, while quantum mechanics suggests that the constituents of matter be discrete; a theory of quantized gravity first has to be realized before the unification. Theories such as string theory and loop quantum gravity are making strides in this unification, however, none of these has produced verifiable predictions yet, and this remains a challenge in modern physics.