I will give the construction of the motivic second Hopf map $\nu$ in terms of framed correspondences and show that the nonvanishing of the corresponding element in generalized motivic cohomology gives an obstruction to the existence of symplectic Thom isomorphisms. As a corollary we will see that the stable $\mathbb{A}^1$-derived category does not admit Thom isomorphisms for oriented (and for symplectic) bundles.