It is often said that that there is a trade–off to be had between liberty and security but in fact the debate has become unnecessarily polarized. Why can we as a society only have one without the other?

This is a false dichotomy. Security is protection from interference and liberty is the absence of interference. Liberty is the result of effective security measures. Where we typically run into problems is when we fail to ask WHOSE security is being improved by implementation of a particular security measure. If you are being asked to give up any liberty in the bargain, then you can rest assured that it isn't your security that is being improved.