So my book says that the batteries we have considered so far( Daniell cells) are low life span, because they reach equilibrium too fast. In the next paragraph, it says they are also made by irreversible reactions and we call them primary battery. I know that the reactants and products of Daniell cell reach equilibrium (Zn+Cu2+ <------> Zn2+ + Cu). How can one reaction reach equilibrium without being reversible?
A battery has a small shelf life if it discharges internally. Saying that a discharged battery is in chemical equillibrium (or much closer to it than a fresh one) is a true statement, obviously, but nothing else.
If you reverse the polarity of a primary battery, you get some other reaction than the one happening during discharging backwards. That says something about that specific battery type, not about the principal reversibility of the basic schoolbook reaction. Typical case is that the electrolyte is electrolysed (e.g. water to hydrogen and oxygen) instead.
You could sometimes avoid that side reaction by e.g. using a lower voltage for charging, but of course then you can only charge the battery up to a few percent or so.