Bibliometric data are relatively simple and describe objective processes of publishing articles and citing others. It seems quite straightforward to define reasonable measures of a researcher's productivity, research quality, or overall performance based on these data. Why do we still have no acceptable bibliometric measures of scientific performance? Instead, there are hundreds of indicators with nobody knowing how to use them. At the same time, an increasing number of researchers and some research fields have been excluded from the standard bibliometric analysis to avoid manifestly contradictive conclusions. I argue that the current biggest problem is the inadequate rule of credit allocation for multiple authored articles in mainstream bibliometrics. Clinging to this historical choice excludes any systematic and logically consistent bibliometrics-based evaluation of researchers, research groups, and institutions. During the last 50 years, several authors have called for a change. Apparently, there are no serious methodologically justified or evidence-based arguments in the favor of the present system. However, there are intractable social, psychological, and economical issues that make adoption of a logically sound counting system almost impossible.