Someone once said that all the teachings of Buddhism can be summarized by one line – “Nothing, whatsoever, should be clung to.” This is one major teaching that each and every one of us has to master before we can attain Enlightenment. However, since “Nothing, whatsoever, should be clung to”, even this teaching should not be clung to. That is to say, we should not cling to “not clinging.” In other words, let go, and let go of letting go. This is not playing with words. Neither is it a paradox. It can be done and has to be achieved in order to attain ultimate freedom.
There are two forms of clinging – that which leads to more clinging, resulting in swirling in the rounds of Samsara in a vicious cycle, or clinging that leads to the freedom of non-clinging – like hanging on to a lifesaver. Just ensure any clinging you have at the moment is of the latter.