It could be that the Joker uses the varying stories to emphasize his unpredictable and chaotic nature. Also, it adds to the mystery and fear around him.
In some comic versions, the Joker's scars origin is a mystery or has multiple conflicting explanations. But in one common story, he claims they were from a traumatic event in his past.
The real story varies depending on different interpretations. In some versions, it's a result of a traumatic childhood. In others, it's linked to his descent into madness.
The origin of the Joker's scars varies depending on the story. Sometimes it's due to a chemical accident; other times, it's part of a more complex and darker backstory.
The Joker does have scars in many comic storylines. These scars can vary in appearance and origin depending on the specific comic. Sometimes they're part of his origin story, adding to his sinister and unpredictable nature.
One possible reason could be that he doesn't want others to pity him. Naruto has always been a proud and strong - willed character. His scars might be a reminder of painful past experiences, and he prefers to deal with them privately rather than showing vulnerability to others.