Same thing with IPv6. I've heard educated people say "It'll be a few more years until we just run out of address space there, too."
Careful there. By design, the IPv6 address space is very sparse. For instance, my house has a /48 netblock allocated to it. If that were the universal rule, the effective address space would be 2^48 networks, not 2^128 hosts. That's also assuming that all of the /48 space is allocated perfectly and densely, and not like a /16 per ISP which would mean that we'd never be able to have more than 66,000 ISPs.
IPv6 will not feasibly support 2^128 hosts because it was never meant for each host to be consecutively numbered. While your coworker is incorrect, your standpoint isn't exactly right, either.