“We wanted it to be faster to use,” Mr. Xu said. On his site, he continued, “You can click on a course, you can see its description, you can see what other students have said about it — all in a few clicks.” In particular, students could sort courses by numerical ratings given by students in previous semesters, and see what courses their Facebook friends were looking at.

It was a success: Last semester, 1,840 students — more than a third of the undergraduate student body — used it to choose their courses, the brothers said. Which is why they were shocked when they got a letter on Jan. 7 from the registrar describing YBB+ as “a big problem.”

University administrators said they were concerned that the site was available to people who were not Yale students, that it gave undue prominence to the numerical ratings without including the descriptive evaluations that went with them, and that it infringed on Yale trademarks. Mr. Xu and Mr. Yu wrote to the registrar offering to fix those three things, along with “4. Anything else you want.”

But Yale opted for more decisive action: It shut the site down.

To Mr. Xu and Mr. Yu, that seemed like a violation of free speech — a right held dear by both academics and Internet activists, many of whom rallied to the brothers’ cause as The Yale Daily News, The Washington Post and other news organizations reported on the shutdown.

Brad Rosen, a lecturer in Yale’s computer science department who teaches “Law, Technology and Culture,” said the debate got at a central tension of contemporary life. “Different stakeholders have different assumptions about how information is going to flow,” he said.