Why is it permissible for Arab men to marry non-Arab women, but a big issue is made when an Arab woman wants to marry a non-Arab man? I read your answer to a question saying there is no distinction between ARAB and NON-ARAB; they are all Muslim. Why should Arab women seek permission from the authorities first?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

In fact the preponderant opinion in the view of the Sharee’ah is that the suitability considered for marriage is religion only. Other than religion, every thing else could be neglected.

A Muslim man can marry any Muslim woman regardless of their lineage. Prophet Muhammad said in this regard: “If a man whose religion and moral conduct are pleasing to you proposes to you, then let him marry; otherwise there will be great mischief and corruption on earth.” [At-Tirmithi]

The practice of the Companions of the Prophet Muhammad certify this opinion. Bilaal (whose origin was not from Arabs) married the sister of Abdur-Rahmaan ibn Awf, who was from the leaders of Quraysh .

As for your question, why a Muslim needs to seek permission from authorities? If you mean by authorities, guardians of a woman, no doubt the guardian of a woman protects her and her rights from the injustice of men. She could be easily deceived by external appearances.

If you mean by authorities, the ruler of the country, then we would like to clarify for you that this rule relates to the man-made rules and these rules do not have any relation to the Islamic rulings except if there is an Islamic legal reason. For example, the authorities may suspect that a foreigner has no intention of marrying the woman for herself and having a permanent marriage. He may have other motives. Such a person may be merely using the woman to achieve other goals.
This is a very common practice. Thus, a woman may in this situation lose an opportunity for marriage with a good man of her own country. It is known that the countrymen usually want to marry women to have a permanent marriage.

Allah knows best.