Why does HCl ionize in water?
Chlorine is a very large atom compared to hydrogen, which means the overlap between the hydrogen $1s$-orbital and the chlorine $sp^3$ orbital is poor, which translates into a low bond energy.

Additionally, chlorine is very electronegative, which helps pull the H-Cl bonding pair onto the chlorine atom. The chloride anion solvation in water also plays a big part.

It's simply because it's energetically favourable. Maybe someone knows in greater detail than I do.