I, with my coathors, have submitted a new draft of our paper “The fallacy of placing confidence in confidence intervals”. This paper is substantially modified from its previous incarnation. Here is the main argument:
“[C]onfidence intervals may not be used as suggested by modern proponents because this usage is not justified by confidence interval theory. If used in the way CI proponents suggest, some CIs will provide severely misleading inferences for the given data; other CIs will not. Because such considerations are outside of CI theory, developers of CIs do not test them, and it is therefore often not known whether a given CI yields a reasonable inference or not. For this reason, we believe that appeal to CI theory is redundant in the best cases, when inferences can be justified outside CI theory, and unwise in the worst cases, when they cannot.”
The document, source code, and all supplementary material is available here on github.