I do not understand; if intimacy is a right for both spouses, then why is that if wife who does not give this right to the husband, he is not obliged to be spent on her? I also heard that intimacy is a return for maintenance; how can this be if intimacy is the right of both?

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. 

The question is not clear. The view of the majority of the scholars of Fiqh is that the intimacy (with the wife) is in return for spending on her, and if the wife refrains from her husband's bed, then she loses her right on her husband to spend on her.

However, some scholars of Fiqh are of the view that her right of spending on her is not dropped by that [i.e. by her refusing to allow her husband to enjoy her in bed].

Ibn Qudaamah quoted both views of the scholars as well as their reasoning, as he said:

"When a wife refrains to share the bed with her husband (i.e. refuses to allow him to enjoy her), or if she goes out of his house without his permission, or refuses to move with him to an accommodation that is similar to that of the women of the same social status like her, or refuses to travel with him, then there is no spending on her, and she has no right on her husband to provide her with accommodation according to the opinion of all the scholars, among whom is Ash-Sha’bi, Hammaad, Maalik, Al-Awzaa’i, Ash-Shaafi'i, the scholars of the Hanafi School, and Abu Thawr. Al-Hakam said, 'She has the right on her husband to spend on her.' Ibn Al-Munthir said, 'I do not know of anyone who has a different view from the above scholars except Al-Hakam; his reasoning is that her disobedience does not exempt her from her right to her dowry, and so it is the same case in regard to spending on her.'

In our view, spending on the wife is only obligatory in return for her allowing her husband to enjoy her; the evidence is that spending on her is not obligatory before she is delivered as a bride to him [i.e. when her husband is enabled to have sexual intercourse with her], and if he does not spend on her, she has the right to refuse to allow him to enjoy her. So if she refuses to allow him to enjoy her, then he has the right to refuse to spend on her, as is the case before he consummates the marriage with her.

As regards the dowry, it is obligatory once the marriage contract is concluded…”

Some scholars of the Maaliki School are of the same opinion as Al-Hakam. Al-Qurtubi said in his Tafseer (exegesis), "Ibn Al-Qaasim disagreed with the opinion of the majority of the scholars in regard to spending on a disobedient and rebellious wife, and he considered spending on her an obligation…"

Nonetheless, the view of the majority of the scholars is stronger, as they have strong evidence to prove and support their opinion.

Allah knows best.