Why do only certain acids disassociate in water?
There are many factors that determine the strength of an acid:


electronegativity of the non-metal atom: an electronegative atom can attract more easily  the electrons of the hydrogen an so generate the proton.
atomic radius greater the radius of the conjugate base greater the acidity, this because the electrons are dispersed around the atom and there is a less attraction between the positive proton and the negative anion.
stability of the conjugate base if the conjugate base is stable due to some particular electronic configuration (e.g. stability due the resonance structure) the species are more prone to be dissociated.