Why should a developer care about Docker?
Probably not the answer that you're looking for, but an answer nonetheless :) 

Learning about docker and its deployment methods could actually be included in the business requirements by making it part of the project or team development environment, just like the code language(s), version control system, compilers, test infrastructure, etc - to work in that team or on that project one needs to know about and use all of these, can't "bring your own" (in most cases).

Things get a bit more complicated if by "a developer" you actually mean the majority of or even entire development team. Pushing a tool in the development environment without actually having any of the developers supporting it will be really tough. Spend the time to create one such supporter first from the team's technical leadership.

Side note: it might also not be necessary for each and every developer in the team to become a docker expert. Pre-established usage recipes wrapped in simple, cheatsheet-ready commands often allow developers to use docker-based solutions without actually knowing too much about their inner workings, which could be fairly acceptable, especially in large teams. Just like being able to contribute code without knowing all the details about how the end-product is being built.