(graphic via Environmental Working Group)
Bisphenol A (BPA), a compound commonly used to make plastic containers and sealants for foods and water, has been found in canned foods in amounts that can cause developmental defects in small children and animals.
Exposure of animals to low doses of BPA has been linked to cancer, abnormal behavior, diabetes and heart disease, infertility, development and reproductive harm, obesity, and early puberty, a known risk factor for breast cancer.
In addition, Bisphenol A disrupts the endocrine system (ie: your hormones) by mimicking estrogen.
It's also worth pointing out that the "fact-checking" website www.bisphenol-a.org is operated by the American Chemistry Council - a lobbying organization for chemical manufacturers. Their section on the safety of the Bisphenol A-based canned food coating in question hasn't been updated since 2002.