We present a theoretical investigation of the chemical reaction SrF
+ SrF $\ensuremath{\rightarrow}$ products, focusing on reactions at ultralow temperatures. We find that bond swapping SrF
+ SrF $\ensuremath{\rightarrow}$ Sr
2 + F2 is energetically forbidden at these temperatures. Rather, the only energetically allowed reaction is SrF
+ SrF $\ensuremath{\rightarrow}$ SrF
2 + Sr, and even then only singlet states of the SrF
2 trimer can form. A calculation along a reduced reaction path demonstrates that this abstraction reaction is barrierless and proceeds by one SrF molecule ``handing off'' a fluorine atom to the other molecule.