The point is that
if, keyword
if electrons were little balls orbiting a nucleus, then they
would radiate EMR and spiral into the nucleus.
But they aren't.
When an object undergoes acceleration it emits EMR - we are not required to know why
That's not true on both counts; only a
charged object undergoing acceleration will emit EMR.
And you already know why: an accelerating charge produces a changing electric field. This produces a changing magnetic field (remember in motors & generators?), which produces a changing electric field, which... etc.
That's what electromagnetic radiation (light etc.) are, changing electric & magnetic fields propagating through space at the speed of light. That's what Maxwell's laws say; they explain how EM waves are created by a changing electric or magnetic field.
Now the point is that Rutherford's model had electrons as little charged balls orbiting around a positive nucleus.
You also already know from year 11 that an object in circular (or it could be elliptical, the circle's not important) motion is undergoing
constant acceleration because it's changing direction.
So since about year 9 you've been thinking of atoms as negatively charged particles (like little balls) orbiting a positively charged nucleus.
But the fact that any accelerating charge produces EMR makes this impossible; the accelerating (orbiting) electrons should just radiate EMR, and in so doing lose energy (since the energy for the EMR has to come from somewhere) and spiral down into the nucleus.
Remember before Rutherford was the "plumb pudding" model which had the electrons embedded int he nucleus. Rutherford's experiments with the alpha particles & gold foil showed that there was in fact a large nucleus in the centre. But as soon as he proposed his new model all the other physicists would have asked "are we supposed to believe that a charged electron is constantly accelerating and not radiating EMR?". His model wasn't very good, really.
That's why Bohr had to come and make a new (though still wrong) model of the atom.