In which SDLC phase will end-user involvement be most extensive and why?

There are two possible answers to this. The first could be requirements analysis, because the requirement analyst needs to know what the end user needs the software to do. Without the end user, the requirement analyst would need to guess at the requirements.

The other could be testing. Without the end user testing the software, he/she/they will have no idea if the software works until he/she/they put it in a production environment.