Fluorine oxidises water to oxygen whereas chlorine & bromine react with water to form corresponding \mathrm{HX}&\mathrm{HOX} acids.
2F2+2H2O→4HF+O2Cl2+H2O→HCl+HOCl
The reaction of I2 with water is nonspontaneous. In fact I– can be oxidised by oxygen in acidic medium. It is why the I– in nature is not present in that much amount as other halides are present in nature.