Several organic mechanisms I know involve [2+2] cycloadditions and retro-[2+2] cycloadditions, namely:
- The Wittig reaction
- Hydroboration of an alkene
- Olefin metathesis (using Grubbs' catalyst)
How are these in accordance with the Woodward–Hoffmann rules? I think that there are two $(4q+2)_s$ components and that's not an odd number, which is the criterion for a reaction to be thermally allowed.