I am having a hard time understanding why it won't be sigma ideal. It is an ideal, that means closure under finite unions holds. Then it should be trivial to see that closure under countable unions hold too. For instance for an ideal J, if $E_1 \in J, \text{and}, E_2 \in J$, then based on the principle of finite unions, $E_1 \cup E_2 \in J$. Now, the sigma-ideals state that if $ E_n \in J, \forall n \in N, then \cup_{n=0}^{n=\infty}E_n \in J$.
I know my reasoning is wrong, I just don't understand why. Perhaps, I am unable to grasp the difference between finite and countable unions.