An alarming number of young Western women are defying their families — and all logic — to join the ISIS barbarians.

As many as 550 of the estimated 3,000 Westerners who have traveled to Syria and Iraq to join the Islamic terrorists are female, according to the Institute for Strategic Dialogue, a London think tank.

It’s the sick siren song of the caliphate that appears to have taken hold of three British schoolgirls, who lied to their East London families last week and casually slipped out of the country on a flight bound for Turkey, believed to be a stopover for those heading to Syria, and ISIS.

The terrified families of Shamima Begum, 15, Kadiza Sultana, 16, and another 15-year-old friend, students at Bethnal Green Academy who are all believed to be Muslims, made an impassioned plea to their wayward daughters on Saturday.

“Mum needs you home,” begged Begum’s older sister, Aklima. “You belong at home with us. Syria is a dangerous place and we don’t want you to go there . . . We understand that you have strong feelings and want to help those you believe are suffering in Syria. You can help from home . . . Please don’t cross the border.”

But why would “straight-A” students from London seek out ISIS, whose brutal MO includes savage beheadings and burning their captives alive?

Some are coerced — but not all, says law professor Jayne Huckerby, head of Duke University’s International Human Rights Clinic.

“Why do they go? In many cases it’s the same reason as men,” Huckerby told The Post.

Some are alienated by harassment or discrimination against Muslims at home, and want to join what they see as a pro-Muslim movement. Some, according to the ISD, enjoy the shocking violence.

The ISD study, which examined the social-media postings of Western women who joined ISIS, found the women “celebrate the violence of ISIS, unequivocally.”

One woman called the beheading video of US Army vet and aid worker Peter Kassig “gut-wrenchingly awesome,” while others called the beheadings “beautiful.”

The women get a sanitized view of life under ISIS via social media, and can be sparked by what Huckerby calls “a sense of adventure.”

“We’re talking constantly about ISIS being brutal, but they’re getting a different story,” she said.

Women are key to ISIS’s effort to build its own state, she says, whether it’s through fundraising, having children, doing certain kinds of work at checkpoints, or simply recruiting more women.

And for some women, there are benefits to joining ISIS. Many are given free housing and food. Few seem bothered by the lack of freedom afforded to women under ISIS rule.

Others find “a sense of camaraderie and sisterhood . . . in ISIS-controlled territory, in contrast to the fake and surface-level relationships they have in the West,” according to the study.

But for women who find that life under ISIS isn’t what they expected, there’s little hope to undo their mistake, Huckerby said.

“There are women who are going there and finding the reality is not what they were sold on social media by ISIS, and they want to come back, but government policies at the moment are not encouraging return,” she said.