"Rosin-based flux is made from extracts of pine tree sap (Colophony) and can cause health problems if fumes from soldering are inhaled. Colophony is composed of roughly 90% resin acid and 10% neutral material. Repeated or prolonged contact with Rosin may cause skin sensitization. Repeated or prolonged inhalation exposure may cause asthma.
When the flux is heated, colophony has been known to generate fumes including aliphatic aldehydes (like formaldehyde) and hydrochloric acid and other gases containing benzene, toluene, styrene, phenol, chlorophenol, and isopropyl alcohol. Short term problems can include nose, sinus, eye and throat irritation and skin rashes, and long-term problems that may include asthma and dermatitis." --
MIT EHS Soldering Safety and Health Guidelines
tl;dr: Pine tree sap can still mess you up when you burn it.