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See its simply the strength of the bonds. The C-X bond is very polar as carbon is attached to a halogen which has a high electronegativity. Now because of the polar nature of the bond, the halogen can easily be extracted from the bond by the H⁺ of a polar protic solvent. Hence the tendency to extract the halogen even increases further due to attraction by H⁺

To break any bond U req. some amount of Energy....

in case of C-X bond it is taken from the solvation of X-ion by +ve polarity of the molecules the polar solvent  (ex: water)..

The ions are covered by the molecules of the solvent from all where and the +ve of these polar molecules come closer to -ve ion...

This interaction b/w the molecules of solute and the ions is called solvation of ions..

this process releases a large amount of energy as +ve and -ve polarity comes closer......and the process is spontaenious...!!!

CHEERS!!