Both calcium hydroxide and ethanol have a hydroxide group, then why isn't ethanol ionic?
No, it is not ionic.
Your doubts are somehow legitimate if you are not aware of the concept of electronegativity. As a rule of thumb if two atoms have similar electronegativity is harder to have ionic bonds. You can use Pauling scale of electronegativity to have some insights on it.

A difference of electronegativity of over 1.7 is likely to be ionic,
and a difference of less than 1.7 is likely to be covalent.
Source: Atkins, Peter; Loretta Jones (1997). Chemistry: Molecules, Matter and Change. New York: W. H. Freeman &amp; Co. pp. 294–295. ISBN 0-7167-3107-X.

This means you will often deal with ionic compounds made of one ion with a strong electronegativity and one with a weak electronegativity. In fact, ions are composed of anions and cations. With a lot of approximations, we can calculate the electronegativity of a group averaging the electronegativities of the components for $\ce{-OH}~\dfrac{3.44 + 2.82}2 = 3.13$.
In your example, $\ce{C2H5OH}$ ethanol the bond is with $\ce{C}$ ( electronegativity 2.55)  so the difference is 0.58 hence covalent. If the bond is with $\ce{Ca}$ (1.00) the difference would be 2.12 which is greater than 1.7 hence is categorized as ionic.
Of course is not always easy to determine if it's ionic or not so in complex cases we can say that it has an ionic character o covalent character.