Homegroup is, at least at present, only possible between Windows 7 Machines, It uses totally separate technologies from the old Workgroup. One of the major differences is the use of IPv6 for communication.
If you wish to communicate with a workgroup windows 7 does have the required backwards compatibility, of course, but this is limited to the Advanced sharing mode of XP.
Homegroups may be made available for vista machines at some time but due to the obsolete nature of XP I would be surprised to see support at any time. Infact the status of xp is now that only security patches will be made no new technologies above those in SP3
You could if you wish point out to your peer and your teacher that membership here is free, and members here are willing to educate