How is dissolving a physical change and not a chemical change?
This is indeed a bit of a grey area. Consider the following: chemical or physical?

$$\ce{Na+ Cl- (aq)  + Ag+ NO3- (aq)   -&gt;  Ag+Cl- (s) + Na+ NO3- (aq)}$$

There is a tendency in more advanced chemistry to view the formation / breaking of ionic lattices as a physical change, because there are no differences in the electron shells of the atoms. Ions are considered as independent species. As such we could consider the sodium and nitrate irrelevant and reduce the above to simply

$$\ce{Ag+ (aq) + Cl- (aq) -&gt; Ag+ Cl- (s)}$$

Note that I have shown the charges all the way through, to indicate that there are no covalent, dative, or metallic bonds made or broken.

Reactions such as these are definitely "chemical":

$$\ce{Na + \frac{1}{2}Cl2 -&gt; Na+ Cl-}$$
(metallic bonds in $\ce{Na}$ and covalent bonds in $\ce{Cl2}$ broken, electron transferred from $\ce{Na}$ to $\ce{Cl}$.)

$$\ce{C2H4 + H2 -&gt; C2H6}$$
(double bond of $\ce{C2H4}$ opened up, bond of $\ce{H2}$ broken, new covalent bonds formed.)

$$\ce{SOCl2 + 2H2O -&gt; H2SO3 + 2HCl}$$ (covalent bonds broken, new bonds made.)

This last reaction sets up another point. It is usually done with excess water, so the products (which are themselves acids) will then dissolve in water, thereby protonating it:

$$\ce{H2SO3 + H2O -&gt; H3O+ + SO3H-}$$ 
$$\ce{HCl + H2O -&gt; H3O+ + Cl-}$$

These particular dissolutions are more likely to be seen as a chemical change than the dissolution of $\ce{Na+Cl-}$, because there is a rearrangement of covalent bonds (even though it's only a $\ce{H+}$ that moves from one molecule to the other.)

Finally, $\ce{H2SO3}$ has another equilibrium, again involving covalent bonds being broken and made, and therefore a chemical change:
$$\ce{H2SO3 -&gt; H2O + SO2 (g)}$$

Conclusion

Making or breaking of metallic, covalent or dative bonds, or the formation/destruction of new ions or molecules, is always considered a chemical change.

The simple dissolution of an ionic salt, where none of the above mentioned bonds are made or broken, and no new ions or molecules are formed/destroyed, is frequently considered a physical change.

Note the care taken to always write $\ce{Na+Cl-}$ (and never $\ce{NaCl}$) in this answer.