Therefore cells must multiply instead. So when we see a "single celled organism" or even a single cell of a multicellular organism, They can only multiply, Not divide. Each cell already contains 2 organisms within 1 membrane. There is simply too much risk to such a simple and small design to "tear itself apart" and create copies of itself. An injury is the last thing a cell would want, And the organism would not be able to evolve as it would grow weak from constantly tearing itself in half which would deplete it's resources. So, Again, When it regenerates the other half of the "cell", It's really just reproducing another "half cell" if you will. The act of asexual reproducing is simply detaching from the other organism. It does not become it's own organism when detached from the other half of the cell membrane it was already it's own separate living being when it was still attached.
Similarly, Sponges are actually not some kind of "living cancer". A sponge is not one thing it is a collection of single cell organisms that have evolved to excrete a material that they can all connect to like a hive. That is why sponges are now considered a colonial organism.
Starfishes have a very similar design to a sponge, Except instead of it being only single cells, It's mainly the arms of the starfish. Only a certain amount of the arm can be regenerated after being torn off which means each arm is basically it's own organism. Of course the missing arm will regenerate the rest of the "starfish" as well as the original "starfish" reproducing a new arm. These arms just happen to be attached to a central hub, Similar to how sponge cells connect to each other.
Life does not want to be injured, . It is in all living thing's best interest to avoid it as much as it possibly can. There are certainly examples of cats for instance the female cats experience great pain when having sex because of the male cats barbed penis but it works because it is recoverable but it does drain the female cat energy. Of course the female cat is not tearing itself in half either.
Living cells split apart becoming two halfs with two copies of the DNA to multiply. Living cells split in two pieces when they multiply which is dividing in two. Its not a tear apart until they become a stretched out cell thats made of two cells that then divides in half to become two cells.