How is Cu(OH)2 a base if it can't dissolve in water? As the title says, how is $\ce{Cu(OH)2}$ a base if it can't dissolve in water?

I mean if it can't dissolve in water then it won't produce any $\ce{OH-}$ ions.

And if it won't produce any $\ce{OH-}$ ions then how can it be called a base?

Same question for $\ce{Fe(OH)2}$ and every other base which is not an alkali.

I feel like this question is quite obvious and don't know how to describe it more. So please help.
Copper (II) hydroxide has some small solubility in water, determined by its solubility product constant.  More importantly, it will dissolve freely and act as a base if a suitable acid, such as acetic acid, is is available to be neutralized.  See also the comment from @f".