What are some solid reasons that I should ask them to buy me a Mac with updated software instead of just a new PC?
To me, it's personal preference and familiarity these days.
I use both Macs and PCs daily so it makes no difference since the software is, to all intents and purposes, identical on both.
Since Illustrator CS2 will not work on newer Macs you would have to ask your new boss to also invest in a new license of Illustrator. They may not even have CS5 and CS2 licenses for Mac, so that would be another investment in terms of time and money for them.
Then there is the problem of supporting Macs on the network and by a company's network administrator(s): they are often WIndows minded, and have a bit of an aversion to Macs, because it makes their lives more difficult.
Thus, in most cases, I found that in a Windows-oriented business environment Macs are generally not welcomed. On top of that, they most probably have service contracts with a vendor like HP or Dell - introducing a Mac only makes things more complicated.
Instead of focusing on the OS, I would check the current configuration of the machine they intend to purchase for you, and make some helpful comments about what specs are REALLY important for a graphic designer, such as a large screen (preferably 2560x1440 screen, multi screen setup) and a hardware calibration device to colour calibrate the screens. A color calibrated soft proof printer. And so on.
Work with them. Not too much against them - you're the new guy at work.
There are probably too many reasons for them NOT to get into Macs.
Of course, you can always bring in your MacBook pro to keep you company ;-)
I teach an InDesign class with both Macs and PCs. They are practically the same, shortcuts and all. The dirty lil secret is CMD on Mac is CTRL on the PC.
It'll be an uphill battle to get a Mac from your boss, and the CS5 suite since CS6 is all you can get now. It's not as big of a deal as you think. I work on a PC at work, Mac at home and in my class. It also makes you more marketable when you can be efficient in both platform environments. It’s WAY easy to use both.