In chapter 1 of The Picture of Dorian Gray, Basil Hallward explains that he does not want to exhibit Dorian's portrait because, as he says, "I really can't exhibit it. I have put too much of myself into it" (Wilde). He further explains to Lord Henry
every portrait that is painted with feeling is a portrait of the artist, not of the sitter. The sitter is merely the accident, the occasion. It is not he who is revealed by the painter; it is rather the painter who, on the coloured canvas, reveals himself. The reason I will not exhibit this picture is that I am afraid that I have shown in it the secret of my own soul. (Wilde)
Basil feels that by painting such a portrait he has revealed his own soul and his own personality. The portrait has become too personal and too intimate to allow strangers to view it. He has poured his own work, heart, and soul into this painting. Basil believes that exhibiting the portrait would somehow be a violation of his own privacy because it reveals too much about him.
Additionally, he goes on to explain to Lord Henry that he feels that the subject of the portrait, Dorian Gray, has become a muse for him. Basil has an obsession with Dorian, and he believes that simply having Dorian around makes him a better painter and allows his art to reach new heights. However, he does not want Dorian or anyone else to guess at "all this curious artistic idolatry"(Wilde) and concludes that "my heart shall never be put under the microscope" (Wilde). Basil does not wish to allow his own feelings or heart to be on display for the public, and he thinks that he would be doing just that if he exhibited the painting.