I assume you're referring to cyclic ozone, which has a Lewis structure that looks like this
Well, I can think of two main reasons for why ozone's molecular stucture cannot be described like that.
This means that the ideal bond angle for a structure that has 2 lone pairs is roughly
This is very similar to what happens for cyclopropane, or
This brings me to the second reason for why cyclic ozone is not the actual structure for the ozone molecule. In one word, polarity.
Notice that such formal charges exist on the two Lewis structures above (the ones labeled "more important"), but do not exist on the cyclic ozone.
In a cyclic structure, ozone would be a nonpolar molecule.
Attempts have been made at producing cyclic ozone, check out this link for more info on that: