To answer your question, we need to first show the job each mirror is doing.
First up, the Newtonian (lovingly called the "Newt", and invented by Sir Ike Newton):
https://en.m.wikipedia.org/wiki/Reflecting_telescope#/media/File%3ANewtonian_telescope2.svg
Two mirrors in this design, not surprisingly labeled as primary and secondary.
The job of the primary mirror is NOT merely to reflect light, but to concentrate the diffuse photons onto a much smaller point. This makes really dim objects brighter, and is the first step in magnification. (Further magnification is done by the eyepiece, which is similar to a small refracting telescope.)
In the case of the Newt, the secondary mirror reflects the now concentrated photons to a more convenient point for viewing. Without the secondary mirror your head would get in the way of the view. A secondary mirror is not necessary, and in fact many telescopes will place instruments, such as CCD's, at this "prime focus" point.
In the case of the Hubble Space Telescope, the secondary mirror reflects the concentrated photons to the scope's instruments, where they can work their magic.
In all reflecting telescope designs the primary mirror uses the laws of physics to give the end user, whether it's the human eye, or research gear, as many concentrated photons as possible, maximizing what we can see/detect. The bigger the primary mirror, the more concentrated the photons, and the more we have to work with.
When it comes to seeing what we call "the dim fuzzies", bigger IS better!
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