During the time of Internet Explorer 9, it was surprisingly common for people to still be using Internet Explorer 6. This was often out of their control, for instance if they had intranet sites that required Internet Explorer 6, or if they were stuck on an old version of Windows because they had outdated hardware.
Later versions of Internet Explorer had compatibility mode, but it often wasn’t enough to get things working, especially if there was ActiveX involved or the security policies were restrictive.
Schools were especially prone to this due to their limited budgets among other reasons, and IT teachers weren’t normally the decision makers who could do anything about it. You shouldn’t assume that a random IT teacher had the authority to spontaneously upgrade a school computer that needs to be used for things besides that one student’s assignment.
I will, however, assume that an IT teacher has the ability to recognise, "this isn't working because I'm using an ancient browser". If the teacher is completely unable to use a less ancient browser, the requirement for the project to work on IE6 should be clearly stated, which it was not.
However in this case, my friend just helped the IT teacher install Google Chrome on his computer and showed that the site rendered fine there. I don't know what sort of policies were in place but there were evidently no technical measures implemented to prevent people from installing a modern browser.
I think your friend might have used portableapps.com, they offer many types of browsers . These programs are packaged to install under a restricted account, without requiring admin rights.
And the IT teacher could have done the same, if he was competent.