Since I never actually answered LLXerxes' question in my earlier posts to this thread, I suppose I should actually answer his question.
Though I disagree with Gainy Bo over whether IE is a good web browser, I agree that you probably won't get anywhere trying to convince the sysadmin to switch the web browsers.
Basically, I see two possibilities:
1) The sysadmin is competant, in which case he knows how to decently secure Internet Explorer (it won't be perfect, because not all vulnerabilities can be worked around in the security settings, but IE can be made somewhat secure by turning off enough "features." In this case, he probably wouldn't want to switch browsers, because of the work he has put into securing IE, and the fact that, because of the work he put into it, the security issue isn't large enough for him to consider switching browsers.
2) The sysadmin is incompetant*, in which case, he probably hasn't secured Internet Explorer, but any argument to convince him to switch browsers wouldn't work because he doesn't care.
Either way, you can try (and I do suggest trying, you might get lucky), but I don't think it'll make it far.
*Note that I am not calling your sysadmin incompetant. I don't know him, I'm just trying to cover all possibilities.