Why NOx will break the ozone sphere
According to Introduction to Atmospheric Chemistry, by Daniel J. Jacob, Princeton University Press, 1999,Chapter 10,

An important component of aircraft exhaust is nitric oxide ($\ce{NO}$) formed by oxidation of atmospheric $\ce{N2}$ at the high temperatures of the aircraft engine. In the stratosphere $\ce{NO}$ reacts rapidly with $\ce{O3}$ to produce $\ce{NO2}$, which then photolyzes:
$$\ce{NO + O3 -&gt; NO2 + O2}$$
$$\ce{NO2 + $h\nu$ -&gt; NO + O}$$

Note that there is no net consumption of $\ce{NO_x}$, thus it is able to act as a catalyst such that a single $\ce{NO_x}$ molecule can destroy many molecules of ozone by these reactions.
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