For magnetohydrodynamic (MHD) flow on a sphere, a `clamshell instability’ exists: field lines on two hemispheres tilt in opposite directions and finally overturn (Cally, Sol. Phys., vol. 199, 2001, pp. 231–249), and this instability has important implications to the magnetic field of the sun. We undertake an analytical study to understand this instability via the method of matched asymptotic expansions. It is shown that when the zonal flow is solid body rotation, there exists a neutral mode that tilts the magnetic field lines, referred to as the ‘tilting mode’. A shear of the zonal flow excites the critical layer of the tilting mode, which reverses the tilting direction to form a clamshell pattern and induces the instability. The asymptotic solution concisely reveals the instability properties for a wide range of flow and field profiles.