According to the award's requirements, the Congressional Space Medal of Honor may be awarded to "any astronaut who, in the performance of his duties, has distinguished himself by exceptionally meritorious efforts and contributions to the welfare of the Nation and mankind."
Is there any specific known reason why Aldrin, and indeed, even Collins, were not afforded this honor alongside Armstrong? Of course Armstrong was the mission commander, and the first man to set foot on the moon, but it's difficult to not consider all of their efforts "exceptionally meritorious" as major pioneers in mankind's space exploration endeavors.