Do acids react with neutral salts? I am new to the concept of neutralization.
My teacher told me that acids do not react with neutral salts.
I want to know why not. 

If both are dissolved in water and both completely dissociate, why can't the ions of acid and salt exchange and perform a double displacement reaction. 

Moreover I have seen the following reaction in a book: $$\ce{2 NaCl + H2SO4 -&gt; 2 HCl + Na2SO4}$$
Neutralization is a reaction between acid and base which results in the formation of a salt and water.
When you have any ionic compound and dissolve it into water, dissociation occurs.
This means that you get a solution of ions.
So if you dissolve acids, bases or salts into water, you end up with a mixture of ions.
Then, more things may happen or not.

In the case of the given reaction, you will get a solution with:

$\ce{Na+ + Cl- + H+ + SO4^{2-}}$

If the system is closed, nothing will happen.
But if the system is open, then $\ce{HCl}$ will evolve because it is a gas.
Since the sulphuric acid is very polar and a liquid, water is not even required.
This is, in fact, the standard procedure to prepare anhydrous HCL in the lab. Just drop $\ce{H2SO4}$ on $\ce{NaCl}$. It must be said that $\ce{NH4Cl}$ works better.