This is an authentic hadîth related in Sahîh Muslim.
The meaning of this hadîth
When the Prophet "peace be upon him" said: "He never spares the rod", it means that he would beat her if she became his wife.
Usâmah b. Zayd b. Hârithah was a freed slave, and therefore had no social status in society. Both Mu`âwiyah and Abû Jahm were of noble breeding and were her social equals. In both cases, the Prophet (peace be upon him) faults them for their characters.
Its legal implications
This hadîth is evidence that equal social status is not a condition for marriage in Islam.
There can be no doubt that, for Muslims, religion is a necessary consideration when it comes to choosing a suitable marriage partner.
Allah says: "Do not marry idolatresses until they believe; for lo! a believing bondwoman is better than an idolatress though she please you; and give not your daughters in marriage to idolaters till they believe, for lo! a believing slave is better than an idolater though he please you." [Sûrah al-Baqarah: 221]
Even when a Muslim man marries a Jewish or Christian woman, her chastity and the uprightness of her character are still important considerations.
We can see this where Allah says: "(Lawful unto you in marriage) are (not only) chaste women who are believers, but chaste women among the People of the Book, revealed before your time,- when ye give them their due dowers, and desire chastity, not lewdness, nor secret intrigues" [Sûrah al-Mâ'idah: 5]
As for equality other matters – like race, ethnicity, and economic status – this is not legally recognized as a condition for marriage in Islamic Law. All people are equal to each other, regardless of how they might differ in these matters. Allah makes it clear that our status in Islam is based solely on righteousness: "Indeed, the most honorable of you with Allah are those who are the most God-fearing among you." [Sûrah al-Hujurât: 13]
The Prophet (peace be upon him) said: "Human beings are equal. There is no preference of an Arab over a non-Arab. Preference is only through piety." [Musnad Ahmad (23489)]
We see where the Prophet (peace be upon him) put this principle into practice when he advised Fâtimah bint Qays to marry the freed slave Usâmah b. Zayd when she came to him for his opinion on her marrying her social equals Mu`âwiyah and Abû Jahm. [Sahîh Muslim (1480)]
On another occasion, the Prophet (peace be upon him) advised: "O clan of Bayâdah, have her marry Abû Hind." [Sunan Abî Dâwûd (2102)] Abû Hind worked as a cupper, carrying out the procedure of medicinal bloodletting, which was an occupation of very low status in Arabian society.
All of the hadîth we have just mentioned are authentic.
We cannot say the same thing for the hadîth which claims that the Prophet (peace be upon him) said: "Arabs are the equals of each other." [Sunan al-Bayhaqî (7/1740]
The chain of transmission for this hadîth is extremely weak. The hadîth scholar Abû Hâtim al-Râzî goes as far as to say it is a falsehood (munkar).
At the same time, we must acknowledge that, when it comes to issues of selecting a marriage partner, cultural standards are important. They should be taken into consideration as long as they do not contradict with Islamic teachings. When people get married who have dissimilar economic or cultural expectations, it can lead to problems in their lives as well as between the in-laws. Divorce becomes more likely, as well as strife over monetary matters.
Incompatible matches, for whatever reason, should be avoided. However, it is a mistake to treat social status, ethnicity, and cultural similarity as if they were conditions of a legally valid marriage, or to allege that the marriage of people who differ in these considerations is frowned upon in Islamic Law. Consideration of such factors is merely a question of compatibility, mutual understanding, and of making a happy marriage choice.