Identify the incorrect statement from the following :

Carbon has a strong tendency to form $p\pi$-$p\pi$ multiple bonds with itself, such as in alkenes and alkynes. Thus, the first statement is correct.

$\text{BCl}_3$ exists as a monomer because boron cannot expand its octet to form a dimer, whereas $\text{AlCl}_3$ exists as a dimer ($\text{Al}_2\text{Cl}_6$) to complete its octet. Thus, the second statement is correct.

The catenation property depends on the element-element bond strength. The bond enthalpy decreases down the group, so the order of catenation is $C >> Si > Ge \approx Sn$. Thus, the third statement is correct.

Oxygen exhibits a $-2$ oxidation state in most of its compounds, but it also exhibits a $-1$ oxidation state in peroxides (e.g., $\text{H}_2\text{O}_2$), a $-1/2$ oxidation state in superoxides (e.g., $\text{KO}_2$), and positive oxidation states when bonded to fluorine (e.g., $+2$ in $\text{OF}_2$ and $+1$ in $\text{O}_2\text{F}_2$). Thus, the fourth statement is incorrect.

Answer: Oxygen exhibits only $-2$ oxidation state.