why is it so important not to be dating in the musilm calture?
because you might enjoy physical pleasure and love with your partner before the social authorities have approved such behaviour.
Muslim culture is often influenced by the teachings of the religion itself. Those teachings are contained in the Quran, the holy book of Islam, and in the body of knowledge that explains the teachings of the Quran called the sacred law or the Sharia.
Now according to the teachings of the religion believers are commanded to be chaste and decent which means, in part, that they are not to engage in inappropriate sexual activity. In the Quran we read:
"Prosperous are the believers who are humble in prayers, who turn away from idle talk,... who protect their private parts except from their spouses and those owned by the right for in them there is no blame..." Quran Ch. 23 verses 1 - 6.
"Don't come near to fornication for it is indeed indecency and an evil way." Quran Ch. 17 verses 32.
"Say to the believing men, that they cast down their gazes and guard their private parts; that is purer for them. God is aware of the things they do. And say to the believing women, that they cast down their gazes and guard their private parts, and reveal not their adornment save such as is normally apparent;" Quran Ch. 24 verses 30 and 31.
So the teachings of the Quran prohibit approaching (coming near) to indecency and fornication, not just the act of fornication itself, and it commands the believers to avoid even gazes that could lead to the act.
Lady Aisha (God be pleased with her), a wife of the Prophet Muhammad (peace be upon him) and one of the greatest of the Religion's scholars, said that the Prophet never touched the hand of an unrelated woman not even those who came to him to pledge allegence (as related in Sahih Muslim 3:1489).
We therefore find in books of Islamic law sections that deal with the prohibition of looking and touching unrelated members of the opposite sex (called al-nazr wa al-mas) which limit the scope of interaction between the genders based on the teachings of the Quran and the example of the Prophet Muhammad.
So because Muslims believe firmly that the Quran is the word of God and because the Quran says what it does about decency and chastity, free mixing of unrelated men and women is prohibited to various degrees in Muslim law, societies, and cultures. Also things like shaking hands and hugging are likewise prohibited. Dating is another form of that kind of prohibited mixing. And so it would be strictly avoided by observant Muslims. I hope that is clear, if not feel free to ask further.