More often than not artists do not give arguments about using the golden ratio, they are sufficiently motivated by the long tradition of singling it out as "golden", which accumulated since Pythagoreans and the ancient Greek sculptor/architect Phidias. The perceived presence of golden ratios in his Parthenon now appears to be spurious, but the letter φ often used to denote it comes from the first letter of his name. Plato helped too by promoting dodecahedron, "which the god used for embroidering the constellations on the whole heaven", and which is full of golden ratios just like the Pythagorean pentagram. Both Pythagoreanism and Platonism flourished during the Renaissance, when much of our modern artistic tradition was forged, and even Copernicus and Kepler were self-proclaimed Pythagoreans. This said, the extent of the ratio's use in arts is greatly exaggerated today. Here is Falbo:
"It is remarkable that prior to Fischler’s and Markowsky’s papers, there seemed to have been no set standards for obtaining measurements of artwork. Often, a proponent of the golden ratio will choose to frame some part of a work of art in an arbitrary way to create the appearance that the artist made use of an approximation of φ. Markowsky shows an example in which Bergamini arbitrarily circumscribes a golden rectangle about the figure of St. Jerome in a painting by Leonardo Da Vinci, cutting off the poor
fellow’s arm in order to make the picture fit."
Livio in The Golden Ratio and Aesthetics is similarly skeptical:
Many books claim that if you draw a rectangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of the height to width of that rectangle is equal to the Golden Ratio. No documentation exists to indicate that Leonardo consciously used the Golden Ratio in the Mona Lisa's composition, nor to where precisely the rectangle should be drawn. Nevertheless, one has to acknowledge the fact that Leonardo was a close personal friend of Luca Pacioli, who published a three-volume treatise on the Golden Ratio in 1509 (entitled Divina Proportione).
The occurence of the ratio in nature is also exaggerated, as Falbo points out, "we find that spirals in sea shells do not generally fit the shape of the golden ratio. This is true despite the numerous articles on the Internet
and elsewhere, in which pictures apparently have been stretched to fit". It is also curious that the ratio was not extracted "from nature" before Pythagoreans, whose interest in it was apparently sparked not by nature but by the "mystical perfection" of the pentagram.
This is not to say that the ratio does not genuinely occur in nature (along with many others), or that some artists did not consciously use it, e.g. Dali in the Sacrament of the Last Supper. Le Corbusier, the architect, developed a whole system of proportions, called Modulor, which "was supposed to provide a standardized system that would automatically confer harmonious proportions to everything, from door handles to high-rise buildings."
Aside from the half-fabricated tradition, a boost to this usage was given by Fechner's psychological experiments in 1860-s, where the participants were shown ten rectangles, and 76% chose as "the most pleasing" the ones with the side ratios of 1.75, 1.62, and 1.50, the 1.62 being closest to the Golden one. Trouble is, later experiments did not reproduce Fechner's findings, and Godkewitsch's meta-study in 1974 concluded that the preference was an artifact. According to Godkewitsch:"The basic question whether there is or is not, in the Western world, a reliable verbally expressed aesthetic preference for a particular ratio between length and width of rectangular shapes can probably be answered negatively". More recent experiments concerning proportions of faces also failed to confirm the golden ratio's hype. As Livio points out:
"The history of art has nevertheless shown that artists who have produced works of truly lasting value are precisely those who have departed from any formal canon for aesthetics. In spite of the Golden Ratio's truly amazing mathematical properties... I believe that we should abandon its application as some sort of universal standard for "beauty", either in the human face or in the arts."
Nick Seewald runs a website on golden ratio, which has a lot of up to date information on its occurences, real and mythical.