If losing electrons means getting oxidized, then does it mean that ALL metals are reducing agents, since they themselves get oxidized?
Your reasoning is sound. All (pure) metals can act as reducing agents, but they do not have to all the time. There are a few examples of metals in negative oxidation states, where they would act as oxidising agent.

Probably the most prominent examples are Zintl phases, where alkaline or earth alkaline metals reduce post transition metals (or metalloids like antimony). One of the first reactions observed was the sodium lead reactions in liquid ammonia in 1907. Back in the day they proposed the following reaction equation:
$$\ce{Na + excess~Pb ~-&gt;[\ce{NH3}][\mathrm{-50^\circ C}]~ Na+ + $“$~Pb2^{-}~$”$}$$
It was later found that the actual composition is $\ce{Na4Pb9}$. With crown ethers and/or cryptants it is possible to isolate discrete anions, too.

There are more examples like this, and a nice overview is given in John E. Ellis, Inorg. Chem., 2006, 45 (8), 3167–3186.