Microscopic structural instabilities of EuTiO3 single crystals were investigated by synchrotron x-ray diffraction. Antiferrodistortive (AFD) oxygen octahedron rotational order was observed alongside Ti derived antiferroelectric distortions. The competition between the two instabilities is reconciled through a cooperatively modulated structure allowing both to coexist. The combination of electric and magnetic fields increases the population of the modulated AFD order, illustrating how the origin of the large magnetoelectric coupling derives from the dynamic equilibrium between AFD and polar instabilities.