Let $C$ be an abelian category and let $X$ an object with finite length.
Then $X$ has a composition series
$$0=X_0<X_1< \cdots X_n=X$$ where $X_i/X_{i-1}$ is simple for $i=1, \dots, n$.
Question Is $X=X_0 \oplus X_1/X_0 \oplus \cdots \oplus X_n/X_{n-1}$?
No. For example, $\mathbb{Z}/p^2\mathbb{Z}$ has a composition series consisting of two copies of $\mathbb{Z}/p\mathbb{Z}$, but it is not isomorphic to $(\mathbb{Z}/p\mathbb{Z})^2$. As in your previous question, this reflects the existence of interesting Ext groups in general (even between simple objects).