how can we say that angular velocity is an axial vector?

Dear Student,

Angular velocity is an axial vector, i.e., under a point of reflection at the origin $\overrightarrow{r}=-\overrightarrow{r}$, it does not change its direction contrary to polar vector like velocity vector and acceleration vector.
$$\begin{gathered} \overrightarrow{r}=-\overrightarrow{r}; \\ \overrightarrow{v}=-\overrightarrow{v} \\ \overrightarrow{\omega }=\overrightarrow{\omega } \end{gathered}$$
The vector product of two polar vector is an axial vector.