Is oxygen's paramagnetism biologically relevant?
It sounds a bit like chem exam question to be honest... Or at least the answer does... namely that O2 being paramagnetic creates a "spin barrier" that prevents most organic compounds from reacting fast with atmospheric oxygen:


  The magnetic properties of O2 are not just a laboratory curiosity; they are absolutely crucial to the existence of life. Because Earth’s atmosphere contains 20% oxygen, all organic compounds, including those that compose our body tissues, should react rapidly with air to form H2O, CO2, and N2 in an exothermic reaction. Fortunately for us, however, this reaction is very, very slow. The reason for the unexpected stability of organic compounds in an oxygen atmosphere is that virtually all organic compounds, as well as H2O, CO2, and N2, have only paired electrons, whereas oxygen has two unpaired electrons. Thus the reaction of O2 with organic compounds to give H2O, CO2, and N2 would require that at least one of the electrons on O2 change its spin during the reaction. This would require a large input of energy, an obstacle that chemists call a spin barrier.


(quote from McQuarrie and Simon's (free) textbook Physical Chemistry: A Molecular Approach).