One of the best ways to keep a shooter game's community alive and well is to release new content for it regularly. One way of doing that is allowing users to create their own content for the game. In the case of Overwatch, that could come in the form of a map editor... eventually.
This is a common issue with new game engines. Making applicable tools for users usually requires a lot of backend support and technical wrangling to get it all working right proper.
Some of you might be asking "Why don't they just make the editor available that the map maker used to make maps for the game?" Well, it's not that simple.
For some games, the map makers are actually pretty user-friendly, even the developer tool version. They can stretch and move geometry, place down objects and set up spawn points with some button presses and mouse movements. However, we don't exactly know what the map tools look like for Overwatch, so we don't know how un-user friendly they are.
For example, some dev tools for creating maps also tie into the script editors. It may require manually coding or scripting in spawn point data and locations to avoid bugs or glitches. Some editors require a lot of object property tweaks and edits, including placing entities around the map. Designers may have to tag entities/objects as static or movable, they may have set up paths for various background objects using a separate editor, or they may require another animation tool in order to have things like moving vehicles, similar to what's featured on the Oasis stage of Overwatch.
The thing is, we don't exactly know what the design process is like exactly for making maps in Overwatch. Sometimes new engines will make things easier for developers, other times it's more complex but it may have a streamlined pipeline to work with other departments. In the case of games like Battlefield 1 or Mirror's Edge: Catalyst, the Frostbite engine is a complex series of tools that requires many different engineers from different departments. It would take a lot of time to simplify some map editors down so that they're usable like the ones from Timesplitters.
So, essentially Blizzard would have to condense the process of making maps in Overwatch so that it's easy enough and user-friendly for the community to make their own maps.
Of course, this is a goal for Blizzard but not something that has any sort of definitive time frame for a release. So there's absolutely no way to know exactly how long Overwatch fans could be waiting before it's released to the public. As noted by Kaplan, it's a "very long road" between designing a map editor and releasing an editor.