Question

Why does using two different enzymes to cut the plasmid prevent the plasmid from reforming a circle without the inserted gene?

Answer 1

Because they do not have compatible sticky ends, to treat both the gene of interest and our plasmid vector with the same restriction enzymes because they would have compatible sticky ends.  The insert has a chance of combining with the plasmid. To ensure efficient digestion, the two recognition sites should be more than 10 base pairs apart.