It is not true that the primary motivation of clients is to demean or oppress women.  I challenge you to link to one survey or study that indicates that it is.

Clients pay for sex because, often, it is the easiest and fastest way to obtain physical pleasure.  Lust of the flesh.  That's all.

Men's sexuality is different from women's.  Men place less emphasis on long-term emotional bonds and more on physical sensuality.  Many more men than women are interested in short-term, impersonal, sexual encounters.  This imbalance creates the demand for prostitution.

Buying sex is not buying a woman.  Selling sex is not selling one's body.  It is a service.  A more intimate and personal service than almost any other, true, and one emotionally difficult for most women.  But it remains a fact that when the client leaves the room, he has no further right to any more sex without paying more.

Many feminists find this hard to believe, but going to a prostitute can feel demeaning to a man as well.  He wants sex.  This desire is not transitory, not fleeting, but deep-seated and powerful.  His own partner may not be willing or able to provide it, or he may not have a partner and lacks the social ability to get one.  

There are thousands - millions - of women physically capable of having sex with him but they will all refuse.  To him, sex is a basic desire, even a need.  To a woman, it is something she will not do with him unless paid.  He leaves with his hormones temporarily satisfied but with the awful feeling that no woman wants him, personally, only his money.