I have always known it is better to get non-bleached, but why it is so important?

Here is the why:  Chlorine bleach paper can contain dioxin and organochlorine residues that can be transferred to food and people in which it comes in contact.  As well, most paper products in the US are bleached with chlorine gas or chlorine derivatives, chemicals that are known to create dioxins as a by-product of the bleaching process.   If you want to learn more about dioxin, please do so.  In summation, it is one of the most toxic chemicals known to us and is associated to several health issues, including cancer and reproductive and developmental issues.

So, why expose yourself to it if you have an option to go without it?