The reason for antiparticles

Why do we need antiparticles in a relativistic quantum theory? I will review the usual arguments based on spacetime symmetries and CPT invariance and show that antiparticles are not particles that travel backwards in time as Feynman claimed. In a recent twitter thread [1], Martin Bauer states that antiparticles are needed in a relativistic quantum theory because if we swap space and time in a quantum scattering process, the particles would travel backward in time and this is a puzzle, forcing us to reinterpret those exotic particles that travel backward in time as antiparticles that travel forward in time. His argument is not valid. First, because applied to classical scattering events it would lead to the conclusion that antiparticles are also necessary in the classical theory, which is not the case. Secondly, because relativity does not establish that space and time are equivalent and can be freely interchanged. It is a common misunderstanding of relativity that space