Typically, they point to the Sotah trial (Trial of Jealously, Trial of Bitter Waters), noting that there was no counterpart test for a man's fidelity, or draw attention to the law stipulations about proving a bride's virginity.
The Sotah trial turns out to be a PROTECTION for women(!), not a double standard:
Num 5.12--the trial of bitter waters (Sotah) is a an amazing provision by God for a woman to publicly clear her name (and indict a dysfunctional husband in the process). This is the procedure invoked by a jealous and/or paranoid husband who suspected his wife of infidelity. God gave this law to protect the woman from physical and economic abuse from a capricious and petty husband. In many of the cultures of that day, men had absolute dictatorial rights over their wives. If they suspected adultery, they were allowed to kill the woman without any appeal on her part. There was not a process of justice, or process where they BOTH had to appear before a higher authority. In fact, in the Code of Hammurabi (c. 1720 BC.), CH 132, women who were suspected of this type of infidelity were required to throw themselves into the Euphrates river--if they drown, they were guilty; if not, they were innocent! (Pritchard, Ancient Near Eastern Texts, p. 171). God would instead provide a public vindication process, before His leaders, his people, and the couple. If the woman was vindicated, the man would bear the stigma of unfounded and paranoid jealousy, and slanderous accusation before his friends/family (with possible legal consequences). Her rights were protected by this very ceremony. This was a very, very advanced pro-women procedure for those times.And the proof of virginity is the same thing--a protection (see the syllabus for discussion on this one).
By comparison, in the other law codes of that time, ANYONE could accuse her and force her to undergo the River Ordeal(!). So, the Laws of Ur-Nammu, 14 [ca. 2100bc, Ur in Sumer]: "If a man accuses the wife of a young man of promiscuity but the River Ordeal clears her..." (LCMAM:18).
The examples given as evidence for a double-standard are simply too weak to support such a conclusion. On the other hand, we have TONS of passages that support (1) a much greater emphasis on male fidelity and (2) preferential treatment for women in disputes of this nature.
Again, the data is simply otherwise--IF there is a double-standard, THEN it is "against" the men!