The inerting system was added to the A320 as a result of a new FAA regulation in 2008:

On 21 July 2008, FAA required operators and manufacturers to incorporate a Flammability Reduction Means (FRM) or Ignition Mitigation Means (IMM) on fuel tanks having a flammability exposure exceeding certain thresholds [...]

^{(Airbus FAST Magazine 44)}

Airbus found that only the centre tank was affected by these thresholds required by the FAA:

AIRBUS COMPLIANCE TO THE RULES

Airbus demonstrated that ‘only the centre tank’ of some of its existing aircraft has fleet average flammability exposure exceeding 7% and is affected by the requirements of the FAR Part 26. There is no necessity to do any modification on other tanks. It concerns the following aircraft:

• A320 Family,
• A330-200, A340-200, A340-300, A340-500, A340-600,
• A300-600.

^{(Airbus FAST Magazine 44)}

What exactly does fleet average flammability exposure mean? The FAA defines it as follows:

the percentage of the flammability exposure evaluation time (FEET) each fuel tank ullage is flammable for a fleet of an airplane type operating over the range of flight lengths in a world-wide range of environmental conditions and fuel properties as defined in this appendix[, which] means the percent of time each fuel tank ullage is flammable for a fleet of an airplane type operating over the range of flight lengths.

^{(FAA Advisory Circular 25.981-2A)}

Since the centre tank is usually used first, it will spend more time empty (or almost empty). Fuel vapour is highly combustible (much more than liquid fuel), so the risk is significantly higher for the centre tank.

The inerting system was added to the A320 as a result of a new FAA regulation in 2008:

On 21 July 2008, FAA required operators and manufacturers to incorporate a Flammability Reduction Means (FRM) or Ignition Mitigation Means (IMM) on fuel tanks having a flammability exposure exceeding certain thresholds [...]

^{(Airbus FAST Magazine 44)}

Airbus found that only the centre tank was affected by these thresholds required by the FAA:

AIRBUS COMPLIANCE TO THE RULES

Airbus demonstrated that ‘only the centre tank’ of some of its existing aircraft has fleet average flammability exposure exceeding 7% and is affected by the requirements of the FAR Part 26. There is no necessity to do any modification on other tanks. It concerns the following aircraft:

• A320 Family,
• A330-200, A340-200, A340-300, A340-500, A340-600,
• A300-600.

^{(Airbus FAST Magazine 44)}

What exactly does fleet average flammability exposure mean? The FAA defines it as follows:

the percentage of the flammability exposure evaluation time (FEET) each fuel tank ullage is flammable for a fleet of an airplane type operating over the range of flight lengths in a world-wide range of environmental conditions and fuel properties as defined in this appendix[, which] means the percent of time each fuel tank ullage is flammable for a fleet of an airplane type operating over the range of flight lengths.

^{(FAA Advisory Circular 25.981-2A)}

Since the centre tank is usually used first, it will spend more time empty (or almost empty). Fuel vapour is highly combustible (much more than liquid fuel), so the risk is significantly higher for the centre tank.

By the way, the system is not really a nitrogen generation system. It only enriches the nitrogen content of some HEPA filtered bleed air to reduce the oxygen content:

Air Separation Module (ASM) description

It is the core of the Inert Gas Generation System. The objective is to reduce the centre wing tank ullage O2 concentration to below 12% during most conditions. Each ASM is a semi-permeable hollow fibre membrane bundle contained in a pressure containment canister. This canister is a cylinder with three ports. There is only one ASM on the A320 Family aircraft, two on the A330-200 and A340-200/300, and three on the A340-500/600.

^{(Airbus FAST Magazine 44)}