You can tell your instructor the question is invalid because it assumes that none of the more modern DNS solutions are being used. In a corporate network using mircosoft servers part of the function of a DHCP server is to register the new IP to the DNS. You can then use peer to peer software all you like. There are a number of other variations on dynamic dns that can solve this issue. Mostly the only one that can't be solved is one related to NAT and port mapping but that is more a NAT issue rather than DHCP. Since the common solution to that problem is to assign a static DHCP address so you can use DHCP and always keep the same address. DHCP itself is not the problem, not using the feature that prevents dynamic assignment of addresses is the issue.
The question should be why can't you use peer to peer software that does not use DNS and ip addresses that are dynamically assigned to machines. This is a old question since there have been work arounds for many years.