Here's why Muslim woman can't marry non-Muslim

Islam guarantees the wife’s rights as part of the Divine law, which is not subject to change and it is binding on the Muslim husband.

As far as the non-Muslim man or husband is concerned, he is either not committed to any religion that has obligatory laws preserving the wife’s rights, or else he follows some man-made laws that may be wrong and are subject to change.

Indeed, if we look closely at the laws concerning the wife’s rights in secular or non-Islamic systems, we will find many contradictions and on-going changes. Under all circumstances, there is no guarantee of freedom of belief or worship for the Muslim woman if she marries a non-Muslim person.

This is a good example of how much Islam cares for women. 

Scholars of Islam are also of the view that a non-Muslim husband will show little regard for his Muslim wife's faith. 

This is because a Muslim man respects and believes in all previous religions and Prophets of God, whereas a non-Muslim does not believe in or acknowledge the Prophet of Islam; instead, a non-Muslim considers Prophet Mohammed to be a false prophet and usually believes in all the fabrications made against Islam and its Prophet. 

Even if a non-Muslim husband does not state it overtly, a Muslim wife will always believe that her husband does not respect her faith. There are no compliments allowed in this situation; it's a matter of principle.

Grand Sheikh (Mufti) at Al Azhar (Egypt)

Grand Sheikh of Al Azhar University, Ahmed al-Tayyeb stated in 2016 that a non-Muslim does not believe in the Prophet Muhammad, and his faith does not mandate him to let his Muslim wife – if he marries her – to practise Islamic rites or respect her religious values.

“Marriage in Islam is not a civil contract as it is with [non-Muslims], but rather a religious bond based on affection between its two ends,” Tayyeb said.

Conclusion

Allah forbade Muslim women from marrying non-Muslim men for a reason. That is to protect their religion and the religion of their children! It's difficult to find unity between a Muslim woman and a non-Muslim man. ALLAH is the most knowledgeable.