I was a fan until I read about the effects on testosterone and gonadal function in some rat studies (no equivalent human studies have been done):
http://www.ncbi.nlm.nih.gov/pubmed/21941943
"GTE at relatively high dose may cause impairment of both the morphological and normal functional status of testis in rodents and thus its consumption at relatively high doses raises concern on male reproductive function in spite of its other beneficial effects."
http://www.ncbi.nlm.nih.gov/pubmed/19330017
"The inhibitory effects of GTE may be explained by the action of its principal component, EGCG, and the presence of a gallate group in its structure seems important for its high efficacy in inhibiting testosterone production."
The amount you get from drinking a few cups a day would hopefully not have the same effect!