Putting a pair of double bonds on the central O would be incorrect for a few reasons. 1. Ozone needs 18 valence electrons, the double bonded structure you suggest has 16 2. An O such as the one you suggest would cause that central atom to have a +2 charge, and that is wrong because ozone is neutral, written as O3. The final reason is #3. This is based on theory. Ozone has a SINGLE bond distance. This is only explained by valence bond theory if a resonance structure is drawn. If we did attempt to draw the structure that you suggest, only a single bond length would be present, and clearly that is wrong. I hope this helps.
Dr. Romano