Pu Yi had a living father at the time, Prince Chun, who was also Manchu royalty. Why not choose him? Instead she chose a two-year-old, who immediately was elevated, in dignity if not in power, above every other person in China, including his father – who, apparently, was not even allowed to live in the palace which Pu Yi was never allowed to leave. It’s very un-Confucian, very un-Chinese, for a child to outrank his father, and to grow up with no paternal guidance. What was she thinking?
Cixi wanted a malleable puppet on the throne. Actually, she went through more than one.
That two-year olds are infinitely easier to control than adults.
At any rate Pu Yi, contrary to the movie, did grow up with some paternal guidance. His father was present as regent until 1911 and then returned to run the shadow court in the forbidden city from 1913 to 1924.
But, she was dying.
Kuang Hsu, who didn’t have any sons of his own, had apparently made arrangements with Cixi and some other people in 1901 saying that if he died without a son of his own, the heir of Prince Chun would become emperor. This was after the Boxer rebellion, the consequence of which that Pu-Chun, who had been heir apparent, was removed from that position, because Prince Tuan had supported the Boxers.
The Dowager Empress had done the same thing before – put a young puppet emperor on the throne so she could rule in his stead – so she was just repeating a maneuver that had worked for her in the past.
But, she was dying. And she knew she was dying.
As to why Prince Chun wasn’t picked was that it was tradition among the Manchu not to let a brother inherit. If the emperor didn’t have a son, he’d adopt someone of the next generation and make him his heir. The only exception to this was Kuang Hsu, who succeeded his brother, but that was only because Cixi’s intervention.