Ouch - that's pretty nasty, and I really feel sorry for you right now!
I'm guessing you've made the call to your union?
I'd start with the pros/cons list right away - as someone mentioned, using an external company can be a nightmare (ie Capita, Natwest, Dell, etc) as they often have their own procedures to follow for a call when it's logged. I've had problems in the past where Dell will just cancel a Work Order I've submitted (Despite a detailed troubleshooting list provided each time) because I've missed a step out on their procedures lists.
I'd put together a list of what EXACTLY your school would be missing out on - something along the lines of:
1) No immediate support available
2) Desktop support available by contacting company, but will take a while to get through to the company
3) Company may not be able to assist via Desktop Support if there is a network/hardware problem with the machine.
4) Site may ask end-user to try out several steps by email/call, and may not assist until a details list of what's happened is given (ie Asset number, application they are using, description of the fault, etc - most of the time we get "Computer isn't working when I do xxxx", so when Teachers realise they'll be expected to get the info to them the first time round, correctly, this may shift).
5) May take 3-5 working days for the Company to arrange for hardware replacement/engineer to attend
6) Hardware moves/replacements will be done at scheduled times in advance - no more calls asking for a quick projector install/PC move. Also means when lil Johnny knocks over a vital piece of kit, it may take days for the replacement to arrive instead of getting Tech to come over with a replacement.
7) The costs may only be marginal, and may well not be worth the effort of having staff there raising tickets with information on, waiting days to get something fixed VS having an on-site tech.
There may well be other points to raise, but I'm out of ideas at the moment. I'm not saying all external companies are like this (Before anyone who is an outsourced tech takes offence), but I'm trying to paint a bleak picture that you might be able to use and put forward as an argument.
It might also be worth taking a look and itemizing what you do on a day-to-day basis, what services you provide, and what you can offer them - it could well be that they're after something in particular, or they'd like you to include something else as part of your day-to-day roles.
Have they definitely sat you down and said "We're outsourcing you", or could this be a sneaky/fumbled attempt at trying to see what you do and what they can get out of you?
Yep happened to me in my former school. I was actually made redundant with an option of take a higher payment if I accepted redundancy or a lower one if they had to force me! My union were very helpful but I really do wonder at the logic or otherwise of replacing in house staff with a company which is after all doing the work because they want to make profit out of it not doing it for the good of the community. We live in a crazy world.
Another point worth raising is all the not-really-IT-but-we-get-asked-them-anyway requests, e.g. how to use a digital camera, or "my projector isn't working" which turns out to be the power isolator switch being off or dead batteries in the remote, plus all the ad-hoc training we give in Word, Excel, SIMS, etc. Will the outsourcing company be willing to take those sorts of questions, and how quickly?
Response time is a good question to raise, as well. If a sufficiently important problem comes in, I will drop whatever I'm doing and deal with that instead, immediately. What would the expected response time be if someone phones the outsourced helpdesk and asks them the same question?
I'm not saying that the school is wrong to consider outsourcing, but they should be aware of the full extent of what you do on a daily basis, rather than the high profile or obvious things like "install new software", "replace broken printers", etc. before making the decision to ensure that they are comparing like for like.
The devil is in the detail - what level of outsourcing are they considering?
Example: a teacher here worked in a school where support requests had to be submitted on the helpdesk, but the helpdesk staff were not located at the school only the technicians. The toner ran out when printing off course work and even though the technicians (and toner cartridges) were in the office next door he had to submit a helpdesk request and then wait for that to be dealt with, prioritised and allocated to the onsite staff.