A man is not allowed to touch a woman for two reasons: 1) He is biblically commanded to avoid all women with the status of nidah (Lev. 18:19). 2) It might lead to improper thoughts, which are rabbinically prohibited (Kesuvos 46a; Shulhan Arukh, Even Ha-Ezer 23:3).
Since a man may not touch a woman, one might conclude that this includes social touching such as shaking hands. If this deduction is correct, it has significant consequences. Standard business etiquette is to shake hands with someone to whom you are introduced. This is much more important than exchanging business cards, and refusing to shake hands is quite shocking and, to many, offensive. A year or two ago, the New York Times Magazine “ethicist” advised a woman to refuse to do business with a man who would not shake her hand for religious reasons. If this is the halakhah, so be it. I am sure that God can find other ways to provide our livelihood. However, the question is whether this really is the halakhah.
It seems to me that there are two issues to discuss.
I. Kirvah She-Lo Be-Derekh Hibbah
The first is exactly what kind of touching is prohibited. The Shakh (Yoreh De’ah 157:10) and Beis Shmuel (Even Ha-Ezer 20:1) disagree over whether touching that yields no pleasure is permissible, with the Shakh ruling leniently. R. Moshe Feinstein (Iggeros Moshe, Even Ha-Ezer vol. 2 no. 14) rules that a man may sit next to a woman on a subway, even if they might touch, because such touching yields no pleasure and is permissible, clearly ruling like the Shakh. The Otzar Ha-Posekim discusses this issue at length and demonstrates the authorities on both sides of the issue. However, R. Shlomo Zalman Braun (She’arim Metzuyanim Ba-Halakhah on Massekhes Avodah Zarah 17a sv. hava menashek, 20b sv. hakha nami), writes that the majority of posekim rule like this Shakh.
II. Shaking and Enjoying
Is there sufficient pleasure in shaking a woman’s hand to render it prohibited, even according to the Shakh? R. Moshe Feinstein repeatedly (Iggeros Moshe, Orah Hayim vol. 1 no. 113; Even Ha-Ezer vol. 1 no. 56) ruled that a man enjoys shaking a woman’s hand and it is therefore prohibited.
As someone who has been shaking women’s hands for years, I simply cannot understand his reasoning. A quick handshake yields no pleasure, and is so quick that it cannot even warm a cold hand. It also indicates no closeness between the two parties and is the equivalent of saying “Hello.” R. Joseph B. Soloveitchik is quoted as having permitted shaking a woman’s hand when necessary, and I once went to the trouble of confirming this from people who asked him directly. R. Mordechai Willig recommends what he calls a “dead fish” handshake — shaking with a limp hand.
Granted, all agree that someone who does feel pleasure from a handshake should refrain from doing so. But a simple handshake does not, normally, give any pleasure.
I would add that this certainly varies based on culture and in some places a handshake might, indeed, be intended to demonstrate affection or closeness. In that case, it would also be forbidden. In this vein, R. Yosef Hayim of Baghdad (Od Yosef Hai 1, Shofetim) permits a woman kissing a man’s hand but not shaking it, because in his culture the latter was considered an affectionate embrace.
I once heard a rabbi, who had previously worked for the OU, speak on this issue. He said that he could not understand why many of his former colleagues would shake hands with women while he went to amazing lengths to avoid shaking hands with women on the few occasions in which it arose. Had he only bothered to ask his colleagues, some of whom can learn circles around him, he might have recognized that (they and) their rabbinic mentors permit this when necessary. (NOTE that this is not intended to imply an OU policy on the subject or that everyone at the OU shakes hands with women.)