Which of these "minimal" semisimple Lie algebras aren't simple?

Question

The semisimple Lie algebras, indexed by their Dynkin diagrams, are classified as direct sums of the algebras

$$ \mathfrak{sl}_{n+1} \quad \mathfrak{so}_{2n+1} \quad \mathfrak{sp}_{2n} \quad \mathfrak{so}_{2n+2} \quad E_6 \quad E_7 \quad E_8 \quad F_4 \quad G_2$$

for $n>0$, where $n$ is the rank of the Lie algebra. Are these not all simple? Why not just call these the simple Lie algebras?

Answer 1

As pointed out in the comments, the odd one out here is $\mathfrak{so}_4$.

$$\mathfrak{so}_4 \cong \mathfrak{so}_3 \oplus \mathfrak{so}_3\,.$$