There is no legitimate health reason to avoid using teflon coated cookware.
There are chemicals used in the manufacture of teflon that are possible carcinogens. Tests show that the chemical is not present in the finished product. The potential danger is to factory workers.
Teflon coated pans can give off a gas if over heated. This gas will cause flu-like symptoms in humans but is not fatal. It is fatal for small birds such as parakeets. The temperature needed to cause such an outgassing are far in excess of what is involved in cooking with a pan. If you left an empty pan on a burner on high and forgot about it, you could eventually have a problem.
Teflon itself is chemically inert. If bits of teflon come off pan and are ingested with food, they pass harmlessly through your body.
If you avoid teflon products "just to be on the safe side" you're missing out on a useful tool unnecessarily.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan