Certain changes in DNA can cause normal breast cells to become cancerous. Doctors are searching for the answer as to what causes cancer (breast and other) today, but nobody is able to put their finger on it.  It’s widely accepted that resveratrol is not the underlying cause for cancer.

Resveratrol, a phytoestrogen found in grapes and red wine, is known to function as an estrogen receptor (ER) agonist, but whether it might also exert antagonist activity is controversial.  There is growing interest in phytoestrogens such as resveratrol as potential cancer chemopreventive agents.  Studies have shown the growth inhibiting tendencies of resveratrol when combating cancer cells, it also has tendencies slow the blood flow, therefore blocking regeneration.

From PubMed: “Resveratrol is considered a potential cancer chemopreventive agent. Resveratrol has been shown to induce transcription via both ERalpha and ERbeta. We observed significantly lower tumor growth, decreased angiogenesis, and increased apoptotic index in ERalpha- ERbeta+ MDA-MB-231 tumors in resveratrol-treated nude mice compared with controls. …  This study supports the potential use of resveratrol as a chemotherapeutic agent in breast cancers.”

So to answer your question in non-medical jargon, It is extremely unlikely that resveratrol is the cause for breast cancer.  It very likely is an inhibitor for the growth of cancer cells and therefore might be part of the solution.  If you currently have breast cancer, consult your doctor before taking resveratrol supplements.