It's very clear to me that you haven't used a really good set of headphones, such as the Beyerdynamic DT-770s or Audio Technica ATH-M50s . And if it's treble you're looking for, the Sony MDR-7506 will give you plenty. All of these headphones will run you RM 400 at least, with the beyers going around RM 600 for a used pair.
It's because headphones usually have a higher impedance compared to earphones.
Hell no I would never agree to that. Your headphone simply isn't a "professional headphone", at least in my point of view.
Oh btw it doesn't matter if you blast music through earphones or headphones, both can destroy your hearing.