Why do Miss Emily and Madam want to to convince the public that the clones had souls in Never Let Me Go?
Miss Emily and Madame share the belief that art reveals the soul of the artist. If the clone's art might be seen as soul revealing, then it could be argued that the clones have souls. If it might be thus proven that clones have souls, it could be argued that the clones have the right to humane treatment throughout life with opportunities for expanding their personal experience through education and creativity.
Humans consider clones to not be feeling, thinking individuals. Therefore, it seems okay to treat them however they want. If the clones were considered human, they would have to have the same rights as humans. No one wants to give clones equal rights. It is hard for most people to consider them equals.
We are never actually given conclusive reasons for this behaviour on the part of Madam and Miss Emily. What we can establish from this text, in which so much remains mysterious or undefined for so long, is that clones were treated as subhuman by humans, as the behaviour of humans towards the clones in the story makes completely clear. Presumably Madam and Miss Emily, frustrated at the way that society was using and exploiting the clones for their own benefit when it was clear that they were just as human as the humans themselves, wanted to try and use Hailsham as the basis for arguing for better treatment for clones. The work that students produced, which is no different in quality or standard from the work that "real" human students would produce, presumably would act as testament to the existence of souls in the clones.
However, given the dependency of human society upon clones and the way that they are needed for their organs, such efforts are doomed for failure, and the clones remain without rights and victims of a human society where they are classed as little more than slaves.