When you start learning a new language, the first words you memorize should be “Yes” and “No”. In Japanese, I believe almost all Japanese learners memorize them as「はい」and「いいえ」. Those are fundamental when you communicate with people. However, when it comes to Japanese, I realized this can be inaccurate.
As far as I know, while I frequently hear「はい」I rarely come across Japanese people who say「いいえ」in daily life. I suspected this might be just my subjective perception, so I looked into it on the Internet. Apparently, many others feel similarly. To be more specific, I normally hear「いえ」for formal talk and「いや」for casual talk instead of 「いいえ」.
This seems like a peculiar phenomenon, but I could easily come up with one of the reasons. This happens maybe because Japanese people are unwilling to say “No” in many situations. As a matter of fact,「いいえ」seems to be used only when we want to emphasize “No”, or when we're mad or upset. Consequently, 「いいえ」has been replaced into 「いえ」and「いや」.
Please let me know if you have different opinions by saying「いえ/いいえ、そんなことはありません」.