Is metallic sodium a strong base? Chemical properties: Sodium metal and sodium amide ($\ce{NaNH2}$ ) are strong bases. They react with ethyne to form sodium acetylide with the liberation of hydrogen gas.

How can a metal considered a base (that too strong)? To act as base it should either donate a pair of electrons (in this case it's single electron) or accept proton or give $\ce{OH-}$ ion but here it's not qualifying any one. So is that statement wrong?

Formation of monosodium ethynide:
$$\ce{HC#CH + Na -&gt; HC#C^-Na+ + 1/2H2}\tag{13.59}$$
Formation of disodium ethynide:
$$\ce{HC#C^-Na+ + Na -&gt; Na+C^{-} #C^-Na+ + 1/2H2}\tag{13.60}$$

Source: NCERT 11, Hydrocarbons, Page 386
No, stricly speaking metallic sodium is not a strong base. Strictly speaking, metallic sodium is not a base at all. (Sodium amide clearly is one, though: due to the amide part.)

Not everything that reacts with an acid is a base. If an acid reacts to form hydrogen and there are no hydrides present, that is a very strong indicator that the reaction was not an acid-base reaction but a redox reaction. And that is what metallic sodium is: a strong reducing agent.

Just because reducing agents can react with acids (proton donors) to generate hydrogen radicals and thus nascent hydrogen gas does not make them bases. For the reaction partner of an acid to be a base, it must accept (and keep!, at least to a certain extent) the proton donated by the acid — or, in the Lewis theory, it must donate an electron pair.