This is where you're confused. I'm not the one picking and choosing. I'm willing to throw out everything Whaley says about what Oswald was wearing inside his cab. YOU are the one insisting Oswald was wearing a jacket inside the cab.
Another reason to doubt Oswald was wearing a jacket post-assassination is that his former landlady spotted him on Cecil McWatters bus shortly after the assassination. She described a hole Oswald had in the elbow of a shirt, a whole that was present in the shirt Oswald was wearing when arrested. Bledsoe could not have seen that hole if Oswald was wearing a jacket.
"Having considered the probabilities as explained in Stombaugh's testimony, the Commission has concluded that the fibers in the tuft on the rifle most probably came from the shirt worn by Oswald when he was arrested, and that this was the same shirt which Oswald wore on the morning of the assassination. Marina Oswald testified that she thought her husband wore this shirt to work on that day. The testimony of those who saw him after the assassination was inconclusive about the color of Oswald's shirt,72 but Mary Bledsoe, a former landlady of Oswald, saw him on a bus approximately 10 minutes after the assassination and identified the shirt as being the one worn by Oswald primarily because of a distinctive hole in the shirt's right elbow. 73 Moreover, the bus transfer which he obtained as he left. the bus was still in the pocket when he was arrested.74 Although Oswald returned to his roominghouse after the assassination and when questioned by the police, claimed to have changed his shirt,75 the evidence indicates that he continued wearing the same shirt which he was wearing all morning and which he was still wearing when arrested."
From pages 124-125 of the Warren Commission Report.
Note to Martin Wiedmann:
This is how one provides a cite to support a statement one has made. I realize it's not possible for you to do this when you have just made something up out of thin air.