My favorite example for this is Don McClean's American Pie

I think its like any information though.
Some people want to interpret and imagine. Some want to know.
An author should put out an explanation separately, rather than forcing it on the public.
Those that seek, will find what they are looking for in the facts,
Those that do not seek, will find what they are looking for inside themselves.

Here is a relevant part of the wiki on American Pie:

When asked what "American Pie" meant, McLean replied, "It means I never have to work again." Later, he more seriously stated "You will find many 'interpretations' of my lyrics but none of them by me... sorry to leave you all on your own like this but long ago I realized that songwriters should make their statements and move on, maintaining a dignified silence."

McLean has generally avoided responding to direct questions about the song, except to acknowledge that he did first learn about Buddy Holly's death while folding newspapers for his paper route on the morning of February 4th, 1959 (referenced in the song with the line "with every paper I deliver").

Despite this, many fans of McLean, amongst others, have attempted an interpretation; at the time of the song's original release in late 1971, many American radio stations released printed interpretations and some devoted entire shows discussing and debating the song's lyrics, resulting in both controversy and intense listener interest in the song.