To a first approximation, the facility of a leaving group may be correlated to the acidity of the leaving group's conjugate acid.
#X^-, X=Cl, Br, I#, are all good leaving groups, as these are all poor bases, as the conjugate bases of strong acid. On the other hand, #F# is a poor leaving group, and #HF# is a relatively poor acid. By this same reasoning, the conjugate acid of hydroxide, water, as a relatively poor acid, suggests that hydroxide would be a poor leaving group.
Most of the time, if we want to remove an hydroxide group, we react the alcohol with #"p-toluenesulfonyl chloride"# to make the sulfonyl ester, i.e.:
#ROH + p-H_3C-C_6H_4SO_3Cl + "base" rarr#
#p-H_3C-C_6H_4SO_3OR + "base"*HCl#
The resonance stabilized sulfonate ester is a good leaving group.