Brain death and organ donation is a matter of life and death. If brain death is not death, then to take organs from a brain-dead person is murder. But if brain death is death, then to refrain from taking organs from a brain-dead person is needlessly allowing several other people to die.
Most people do not pasken this question for themselves; instead, they follow their Poskim. But the problem is that poskim on this issue are usually implementing a non-rationalist approach. For people in the charedi world, this is any case usually their own preferred approach. Non-charedim, on the other hand, will follow a posek such as Rav Bleich. Because he writes with sophisticated English (and Latin), has academic credentials, publishes in Tradition, and teaches in YU, these people assume that he reflects their own approach to Torah and Judaism and their own epistemology. But Rabbi Bleich's ruling against organ donation is fundamentally resulting from the same non-rationalist approach that makes him refuse to accept that Chazal mistakenly believed in spontaneous generation.
Rabbi Bleich's methodology for paskening brain death and organ donation is based upon drawing inferences from Chazal, Rishonim and Acharonim. But this only makes sense if Chazal, Rishonim and Acharonim dealt with the relative significance of the neurological and cardiopulmonary systems, and understood the roles of each. Only then could we determine whether they believed life to depend upon the action of the heart or the action of the brain.
But Chazal, Rishonim and Acharonim did not and could not have dealt with the relative significance of the neurological and cardiopulmonary systems. For until very recently, the systems were inseparable. There was no such thing as being brain-dead but having your heart still beating. And furthermore, even if Chazal, Rishonim and Acharonim were to have dealt with the relative significance of the neurological and cardiopulmonary systems, this would be hampered by the fact that they mistakenly believed significant components of the mind to be housed in the heart.
Someone who acknowledges that Chazal only possessed the limited scientific knowledge of their era will (hopefully) take this into account. But if someone believes that Chazal could not have been mistaken about scientific matters - as demonstrated by their refusing to accept that Chazal mistakenly believed in spontaneous generation - then they will refuse to consider that brain death cannot be resolved via drawing inferences from the statements of Chazal.
Recently, a new book was published on brain death and organ donation, entitled "Defining the Moment: Understanding Brain Death in Halakhah," which bears an enthusiastic endorsement from Rabbi Bleich. On a post at the Hirhurim website regarding the launch of this book, I asked the author the following question:
It seems that all those who wrote haskamos, and whose positions you discuss, take the approach of paskening this question directly from the Gemara and earlier poskim. Applying this methodology of psak is in turn is based on two presumptions: that Chazal differentiated between the nervous system and the cardiopulmonary system – and that they correctly understood the role of each. Do you discuss the nature and validity of these presumptions in the book?
I posed this question to the author twice, and despite the fact that he was responding to other comments, he did not respond to my question. My guess is that he'd never thought about it, and is uncomfortable with it. I don't blame him for his discomfort.
If you accept that all the Rishonim, Acharonim and contemporary non-fundamentalist Talmud scholars are correct in understanding Chazal as describing spontaneous generation, and you accept that spontaneous generation has been adequately disproved, you should not be following a ruling regarding being an organ donor from someone who does not acknowledge these points, or who does not incorporate them into his analysis of the issue.