Why do larger aircraft need two or more static ports?
Your quote already answers your question:


  larger aircraft with redundant systems will have two.


The key is redundancy. You want to have at least two independent systems to measure altitude and airspeed so if one fails, the other still provides good data. Of course redundancy is also a good thing in a small aircraft, but it always comes at a cost: complexity. With larger aircraft the added complexity and therefore maintenance cost does not make such a large difference any more therefore tipping the balance in favor of redundancy.

For passenger airliners with potentially hundreds of people on board, safety is far more important. They usually have even more than two static ports. E.g. the Boeing 737:


  Air Data
  
  The pitot static system is comprised of three separate pitot probes and six flush
  static ports. Two pitot probes and four static ports interface with the air data
  modules. The remaining auxiliary pitot probe and alternate static ports provide
  pitot and static pressure to the standby instruments. The auxiliary pitot probe is
  located on the first officer’s side of the airplane.
  
  The air data modules convert pneumatic pressure to electrical signals and send
  these data to the ADIRUs. Each pitot air data module is connected to its on–side
  pitot probe; there is no cross connection. The air data module connected to the
  Captain’s pitot probe sends information to the left ADIRU, while the air data
  module connected to the First Officer’s pitot probe sends information to the right
  ADIRU. The remaining air data modules are located at the balance centers of the
  Captain’s and First Officer’s static ports. The air data module connected to the
  Captain’s static ports sends information to the left ADIRU, while the air data
  module connected to the First Officer’s static ports sends information to the right ADIRU.


(Boeing 737 NG FCOMv2 10.20.13 Flight Instruments, Displays - EFIS/Map System Description, emphasis mine)

This results in three independent measurements of altitude and airspeed: 


Captain's side
First Officer's side
Standby Instruments