Because nothing exists, nothing also does not exist.
In physics especially astrophysics- 'nothing' exists...the example is 'dark matter'.
The scientific workers do not get anything in the space between stellar objects.
However, the presence is felt by the theoretical calculations..and its name is 'dark matter' as when one observes there is 'nothing' to be found.
So, the corollary that nothing' does not exist may not be true.
This type of situation has come earlier also - say before the discovery of 'positron' particle -which is anti-particle of an electron.
The theoretical evidence was there but its detection had not taken place.
If you look at nothing as the opposite of something. The existence of one requires the existence of the other.
the above is true.
But since one explicitly says it is nothing i.e. does not exist. That should also mean that something also does not exists. Or nothing exists.
the above paradox is not there at least in physical sciences.