Why does Basil try to destroy the canvas?

The portrait was originally beautiful - as Dorian was at the time. Basil found that it was creating discord between his friends

• Dorian and Harry - and he did not want that.

As the story tells it:

"Harry, I can't quarrel with my two best friends at once, but between you both you have made me hate the finest piece of work I have ever done, and I will destroy it. What is it but canvas and colour? I will not let it come across our three lives and mar them."

In Dorian, it brought about sadness that the painting would remain beautiful while he aged and decayed - to the point where Dorian swore he would give his own soul to have it switched so that he remained intact while the painting decayed (which is what happened).

Harry coveted the beauty of the painting and wanted it for himself - because he hedonistically sought what pleased him without regard for cost or consequences.