I'm sure it was over-dramatized in the film (which I haven't seen, I'm just assuming they prioritized compelling storytelling based on the fact that it wasn't a public television documentary), but supposedly something like that decisionmaking process actually happened. For example, see Wikipedia's synopsis of the book, which was presumably at least somewhat more factual (https://en.wikipedia.org/wiki/The_Right_Stuff_(book)#Book):
The storyline also involves the political reasons for putting people into space, asserting that the Mercury astronauts were actually a burden to the program and were only sent up for promotional reasons. Reasons for including living beings in spacecraft are barely touched upon, but the first option considered was to use a chimpanzee (and, indeed, chimpanzees were sent up first).
Another option considered was using athletes already accustomed to physical stress, such as circus trapeze artists. Wolfe states that President Dwight D. Eisenhower, however, insisted on pilots, even though the first crew members would not actually fly the spacecraft.
The storyline also involves the political reasons for putting people into space, asserting that the Mercury astronauts were actually a burden to the program and were only sent up for promotional reasons. Reasons for including living beings in spacecraft are barely touched upon, but the first option considered was to use a chimpanzee (and, indeed, chimpanzees were sent up first).
Another option considered was using athletes already accustomed to physical stress, such as circus trapeze artists. Wolfe states that President Dwight D. Eisenhower, however, insisted on pilots, even though the first crew members would not actually fly the spacecraft.