The Northridge quake in 1994 was the event that caused insurance companies to flee the earthquake insurance market, since earthquakes are very rare events that have the potential of causing large losses at one time (as the Northridge quake did), making it difficult to assess insurance risks on them*. California law at the time required homeowners insurance companies to offer earthquake insurance, but many insurance companies stopped or threatened to stop issuing new policies or leave the state entirely because they did not want to deal with earthquake risks. The CEA was created as a result, and most homeowner insurance companies resold CEA policies.
*Note that floods are similar types of risks from an insurance standpoint, which is likely why there is government flood insurance.