Working with any technology you work with people who fall into many categories; people who fear technology, people don't have experience, and others that have equipment that is just outdated or incompatible. Granted, I loved Windows XP and it was a great, stable Operating System (OS) and I also loved my Atari and even my old Sony Betamax but with an Internet Browser there is are a lot more ways the external world can access and potentially harm you. There are many reasons to stay with an old OS or Browser, which we can discuss over wine at another time, but, there are real privacy and security implications related to using an old internet browser on the web.
You might have legacy applications that requires an older browser but you should get a different, modern browser, to surf the web and to use web applications. This is true regardless of the browser you use (Firefox, Chrome, Safari, Internet Explorer). There is also regular maintenance you should do that can help protect your system (upgrading your browser, deleting cookies, deleting cache, etc). At SourceYourMeeting.com we have helped hundreds of hotels accomplish each of these and we regularly hear "I didn't know anyo f this, you are saving the hotel industry one hotel at a time, thank you".
On that note, below is an article about Microsoft's browsers. They have been supporting legacy browsers for long beyond a reasonable life but with the continual evolution of the web they can't support old browsers forever. Effective today, Microsoft officially ends support for all but the latest version of Internet Explorer.