Rails has_one :through association: setting the associated object will delete the joined object.

I have

class CarpoolGroup < ActiveRecord::Base
  has_many :cars
end

class Car < ActiveRecord::Base
  belongs_to :carpool_group
  has_many :car_types
end

class CarType < ActiveRecord::Base
  has_one :carpool_group, through: :car
end

When I set

cat_type.carpool_group = nil

or when I save the carpool_group, the joined Car object got deleted from the DB. I see the SQL DELETE from "cars" where ... after I set car_type.carpool_group = nil.

How do I keep the has_one through association and avoid this deletion?