What is the reason that some people (specifically AFAIK some of Arabs and Kurds) keep their Mustache long, but cut their beard?
My question is that whether it is considered as an Islamic custom? I also want to know regarding the permissible size of Mustache. (Minimum and maximum size)
No, long-mustache is not an Islamic custom. Instead, the Islamic custom is to trim the mustache which is established by the Prophet (pbuh) himself.
It was narrated that Anas bin Malik said:
وُقِّتَ لَنَا فِي قَصِّ الشَّارِبِ وَحَلْقِ الْعَانَةِ وَنَتْفِ الإِبْطِ وَتَقْلِيمِ الأَظْفَارِ أَنْ لاَ نَتْرُكَ أَكْثَرَ مِنْ أَرْبَعِينَ لَيْلَةً
"We were given a time limit with regard to trimming the mustache, shaving the pubic hairs, plucking the armpit hairs and clipping the nails. We were not to leave that for more than forty days." Muslim
The words for 'trimming the mustache' in the hadith are قَصّ الشَّارِبِ which literally means clipping of the drinkers. According to Lisaan-ul-Arab (لسان العرب), the famous Arabic dictionary الشَّارِبِ means ما سالَ على الفَم من الشَّعر i.e. those hair which flow over the mouth. The mustache hair when long tend to touch ("drink") the water we are drinking. That's why they are named so. From this the maximum length can be inferred i.e. the hair should be short enough not to touch the water while drinking.
