VOCs include a variety of chemicals, some of which may have short and long-term adverse health effects. Concentrations of many VOCs are consistently higher indoors (up to ten times higher) than outdoors. VOCs are emitted by a wide array of products numbering in the thousands.
Health effects may include:
Eye, nose and throat irritation
Headaches, loss of coordination and nausea
Damage to liver, kidney and central nervous system
Some organics can cause cancer in animals, some are suspected or known to cause cancer in humans.
There are many organic chemicals where fumes are not harmful, and many inorganic chemicals where fumes are harmful. It is not accurate to conclude that a chemical compound is harmful (or not) based on being organic or not.