Chemistry - Why is nitric acid such a strong oxidizing agent?

Because, unlike in other metal dissolution reactions, the $\ce{H+}$ of $\ce{HNO3}$ isn't reduced—the $\ce{NO3-}$ is. The following data and balanced reactions are taken from Wikipedia:

\begin{align} \ce{NO3- + 4 H+ + 3 e- &-> NO + 2 H2O} & E^\circ_\mathrm{red} &= \pu{0.96 V} \\ \ce{NO3- + 2 H+ + e- &-> NO2 + H2O} & E^\circ_\mathrm{red} &= \pu{0.79 V} \\ \ce{Ag+(aq) + e- &-> Ag(s)} & E^\circ_\mathrm{red} &= \pu{0.799 V} \end{align}

Since the standard reduction potential (SRP) of the $\ce{NO2}$ reaction looks smaller than that of $\ce{Ag+}$ (I may be wrong, but by significant digits it can't be greater than $0.799$), one can conclude that it's the $\ce{NO}$ reaction that's occurring here. And the $\ce{NO}$ reaction has a large enough SRP to oxidise $\ce{Ag+}$.

Usually nitrogen compounds are pretty versatile when it comes to redox reactions, since nitrogen shows many oxidation states. So the simple reason for why $\ce{HNO3}$ is so strong an oxidising agent (with respect to other acids) is that it has a different, better path available to it to get reduced.

Note that the exact reduction path (i.e. final reduction products/oxidation state) depends upon the concentration of nitric acid—so much that copper can be oxidised in three different ways.