Einstein's fundamental rationality-killing step: "the rescaled "local time" variable t' of Lorentz was "purely and simply, the time", as experienced by a moving observer":

http://www.bourbaphy.fr/damourtemps.pdf
Thibault Damour: "Textbook presentations of Special Relativity often fail to convey the revolutionary nature, with respect to the "common conception of time", of the seminal paper of Einstein in June 1905. It is true that many of the equations, and mathematical considerations, of this paper were also contained in a 1904 paper of Lorentz, and in two papers of Poincare submitted in June and July 1905. It is also true that the central informational core of a physical theory is defined by its fundamental equations, and that for some theories (notably Quantum Mechanics) the fundamental equations were discovered before their physical interpretation. However, in the case of Special Relativity, the egregious merit of Einstein was, apart from his new mathematical results and his new physical predictions (notably about the comparison of the readings of clocks which have moved with respect to each other) the conceptual breakthrough that the rescaled "local time" variable t' of Lorentz was "purely and simply, the time", as experienced by a moving observer. This new conceptualization of time implied a deep upheaval of the common conception of time. Max Planck immediately realized this and said, later, that Einstein's breakthrough exceeded in audacity everything that had been accomplished so far in speculative science, and that the idea of non-Euclidean geometries was, by comparison, mere "child's play"."

Poincaré could not take that step, although the Lorentz transforms (of which he was one of the authors) urged him to do so - the step led to the absurd conclusion that, as the observer starts moving towards the light source and, accordingly, the wavecrests start hitting him more frequently, the speed of the wavecrests relative to the observer nevertheless remains unchanged:

http://www.persee.fr/web/revues/home..._num_55_1_2143
Les écrits épistémologiques de Poincaré, obstacles à la diffusion de la relativité?, Vincent Borella, p. 74: "Pour Einstein le postulat de la constance de la vitesse de la lumière par rapport à n'importe quel référentiel dans lequel elle est mesurée (ce qui est une expression du principe de relativité) est suffisant, alors qu'en fait, pour Poincaré, la vitesse de la lumière ne peut être constante que relativement au milieu dans lequel elle se propage, à savoir l'éther supposé immobile."

http://www.jstor.org/stable/3653092
The Mystery of the Einstein-Poincaré Connection, Olivier Darrigol: "It is clear from the context that Poincaré meant here to apply the postulate [of constancy of the speed of light] only in an ether-bound frame, in which case he could indeed state that it had been "accepted by everybody." In 1900 and in later writings he defined the apparent time of a moving observer in such a way that the velocity of light measured by this observer would be the same as if he were at rest (with respect to the ether). This does not mean, however, that he meant the postulate to apply in any inertial frame. From his point of view, the true velocity of light in a moving frame was not a constant but was given by the Galilean law of addition of velocities."

Pentcho Valev