your workmate sounds like a dumbass.
it doesn't sound like he is ignorant, but stubborn, which is a dozen times worse in a workplace where you are responsible for stuff.
I suppose it's not my place to tell him how to do his job, but it seems he is a little lax about his responsibilities...
anyway, as the dudes said, linux is secure because whenever a hole pops up, somebody fixes it pronto, because they can see it immediately.
There are many more honest developers than malicious crackers, so a hole will usually get fixed before any pain is caused, with windows, M$ don't give a shit about upkeep, so they keep it all closed source, hope nobody figures out all their errors ad back doors, and when somebody does, they release a "free" patch that you will probably end up paying for anyway (post, packing, cost of CD, cost of 'required components' et cetera...)
sorry, didn't mean to piss on yr bonfire, if something's not broke, why fix it? (i refer to yr work setup) but open source unix is more secure than a closed winDOS type OS for that and many other reasons.