Whey vs Soy... have we been tricked?

That may be what the author(s) is (are) trying to make you believe, but it’s simply not true.

The affinity of daidzein for the estrogen receptor (ER) is, indeed, more than 1000 times lower than that of estrogen. As suggested, it will thus only outcompete the latter if present at a > 1000-fold higher concentration.

The strength of the signal caused by daidzein binding to estrogen receptor alpha (as measured by binding of the engaged receptor to the estrogen response element) is 30,000 fold weaker than that caused by estrogen. Daidzein binding to ER beta, however, produces a signal that is only about 50 times weaker. While the response to ER beta binding may be somewhat different to that of ER alpha binding, it is thus not correct to postulate that the relative signal strength induced by daidzein is less than its relative affinity for the ER. Moreover, daidzein can be metabolised to equol which then is also a strong agonist of ER alpha.

Where studies show an estrogen blocking effect, they used cells grown in the presence of very high doses of daidzein. The effect was that these cells increased their estrogen production because their estrogen receptors were blocked by the massive amounts of daidzein thus interfering with their ability to determine true estrogen concentrations and thereby eliminating negative feedback mechanisms.