Consider this spurious argument for a possible necessary being:

(∃x)(Fx v ~Fx) holds at every possible world (it's a theorem of first-order logic). Hence, at least one being exists in every possible world. For any concrete, contingent being and any possible world at which that being exists, the world obtained by subtracting that being is possible. Hence, a world with no contingent beings is possible. Every being is either contingent or not-contingent. Hence, there is a possible world where a not-contingent being exists. Hence, there is a possible world where a necessary being exists. 

We're probably not going to deny that the laws of logic hold at every possible world. At least, this would undermine possible worlds semantics and make it hard to make any further claims about these other worlds. 

The second premise is a weak subtraction principle. All it says is that contingent beings can fail to exist without new beings having to exist. There are debates over subtraction principles, but this version seems to follow pretty much straight from what it means to be contingent. 

The third premise is an instance of the law of the excluded middle.

What's wrong with this argument?