According to many reliable reports appearing in the most reliable works of Hadīth like Sahīh of Bukhārī and Sahīh of Muslim the Holy Prophet (sws) used to do Raf‘u’l-yadayn (raising hands up to one’s shouders) when starting the prayer, going to Ruku‘, standing from it, and standing after saying Tashahhud. So I am confused as to why we are not supposed to do Raf‘u’l-yadayn on other occasion besides starting the prayer when the Holy Prophet (sws) did?

The entire structure of prayer was taught by the Holy Prophet (sws) to the entire generation of the companions. All the people of the time of the Holy Prophet (sws) must have known the exact method of the prayer. This structure has been reported down by the collectivity of the Muslims without a break. You know that people never stopped praying and the act of praying is not a concealed one. This has always been a living tradition among the Muslim community. Thus we have the form of the prayer exactly as the Holy Prophet (sws) left it with us. It has been preserved and reported down through the most reliable source of knowledge. This profoundly established practice is countered by a couple of individual reports. We cannot question the authenticity of the report transmitted by the generations of the Muslims Ummah by the individual reports. We are bound to give some explanation to the individual reports appearing in Sahīh of Bukhārī and other works of Hadīth. I think the reporters who transmitted the reports must have reported some previous practice of the Holy Prophet (sws) which he abandoned and left the prayer in the final and ultimate form as it is with us.  However, it should be noted that this also indicates to the fact that the practice of raising both hands at different occasions (other than at the beginning of the prayer) is not a necessary part of the prayer. That is why we see that the Prophet (sws) after initially doing it later abandoned it but did not make sure to eliminate it from the practice.