ERBIL, Iraq — “Before Mosul and after Mosul.” Iraqi Kurdish leaders have taken turns repeating this mantra after capturing vast swaths of disputed territories, including their “Jerusalem,” the oil-rich province of Kirkuk.

Their message is clear. After the dramatic fall of Mosul to Islamic State of Iraq and al-Sham (ISIS) fighters, Iraq cannot be glued back together again. Nechirvan Barzani, the prime minister of the Iraqi Kurdistan Regional Government (KRG), put it to the BBC like this: “I think it will be very difficult for [the] situation to go back as before. I don’t think it [Iraq] can stay together again.”

Coupled with the Iraqi Kurds’ fresh territorial gains, statements such as these have prompted a flurry of punditry, much of it concluding that the Iraqi Kurds are on the brink of declaring independence.

Fellow Al-Monitor columnist Denise Natali provided an eloquent counterpoint to such assertions in her article “Iraqi Kurds maneuver between Maliki and Mosul.” After a trip to Iraqi Kurdistan where I met with various senior Iraqi Kurdish leaders, I tend to agree with some of Natali’s arguments. Despite the Kurds’ territorial windfalls, there remain serious obstacles to independence. Indeed, it is questionable whether it is a realistic goal in the short term.