Here's another argument* against the continuum being composed of indivisibles. An indivisible has a magnitude of zero. Thus adding the magnitudes of indivisibles will always result in a magnitude of zero. For, obviously, zero plus zero is zero. But anything which does have a magnitude, can only be composed of things which have magnitude when added.
Someone objects that this is only true when there are finite additions, or merely countably infinite additions. I don't understand enough of the subject to reply.
*Philosophers always refer to their arguments as 'arguments' and never as 'proofs'. This is because there is nothing in the entire, nearly three thousand year history of philosophy that would count as a proof of anything. Nothing.