Why do transition metals exhibit variable valencies?

• The transition elements exhibit variable valencies because the number of unpaired electrons present in the $(n-1)d$ shells is higher.
• The $(n-1)d$ shells are closer to the outermost $\mathrm{ns}$ shell.
• Hence, the electrons from $(n-1)d$ orbitals can take part in reactions.

This is the reason why transition elements show variable valencies.