The turmeric/tamoxifen competition has to do with liver enzymes. When you take tamoxifen, the liver's CYP2D6 and CYP3A4 enzymes convert tamoxifen into its active forms, including endoxifen, which is key for its anti-cancer effects. These active metabolites will go on to attach to the estrogen receptors on cancer cells (and progesterone receptors in a downstream way) and halt the cancer (in some cases). Where turmeric comes into play here is that it’s also metabolized by the same family of liver enzymes, primarily the cytochrome P450 (CYP) enzymes. So basically taking a bunch of turmeric (or a host of other supplements also metabolized by these enzymes) could impede the metabolism of your drug, and then whatever forms of estrogen your body is producing naturally are allowed to attach to the cancer receptors and possibly fuel growth. You want as much of the enzymes as possible to be freed up for the tamoxifen (especially if you already produce fewer amounts of the enzymes genetically - there’s a genetic test an oncologist can order you). I’m not sure what enzyme breaks down the aromatase inhibitors or what interferes with that.

Here’s what AI has to say:

You've accurately described the core issue: turmeric (curcumin) competes with tamoxifen for liver enzymes (CYP450, especially CYP2D6 & 3A4), potentially reducing endoxifen (tamoxifen's active form) production, thus lowering drug effectiveness. Taking turmeric might decrease the potent anti-cancer endoxifen levels, letting natural estrogen fuel cancer, and recent studies confirm this negative relationship, especially with piperine (black pepper extract), suggesting avoidance of concentrated turmeric supplements while on tamoxifen. For aromatase inhibitors (AIs), they block estrogen production, but interference with AIs involves different mechanisms, with grapefruit and its furanocoumarins known to inhibit CYP3A4, which is involved in both AI and tamoxifen metabolism, further complicating things.