Why is ethyl acetate insoluble in water?
Are you sure that it is?
The literature I have at moment suggests a 10% by mass solubility in water. Of course while the molecule is polar, you got a carbon chain that extends over 5 atoms....and this limits its aqueous solubility.
At ambient temperature ethyl acetate dissolves at roughly 8.5g per 100 ml of water (so 8.5% w/w).....
"Insoluble" means "not soluble at all" - percentage solubility basically = 0.0000%. There are materials that are genuinely insoluble in water (copper oxide, for example).
There are also substances that are often labelled as "insoluble in water" (especially in school chemistry classes) but where the reality is that they are not "insoluble" just "very sparingly soluble".
Calcium carbonate, for example, is often regarded as "insoluble in water" when it actually dissolves at 0.013 g per litre of water. Very small, yes, but it's not zero.
So ethyl acetate, which dissolves in water at ambient temperature at around 8.5% w/w exhibits quite a low solubility, but definitely not "zero solubility". One reason for the low solubility is that the molecule does not contain hydrogen atoms sufficiently polarised to readily form hydrogen bonds with water (unlike ethanol, for example).