It's been spotted by users that on several Youtube channels there's a new option available under the Share section: GIF Creator. I believe the feature will be welcomed by many when it becomes widely available, it's been something people have been wanting for a couple of years now. The proof is quite visible: websites that let you do exactly that - create GIFs from a part of a Youtube video - are quite popular. And it seems like Youtube decided to get back the audience they were losing due to a simple, yet desirable, missing feature.
There haven't been any official announcements just yet, but I encourage you to go ahead and try out the feature. It works quite fast and intuitive, and when the processing is done, you are given a direct URL to the created GIF and the HTML code you need to use to embed the image on a website. At the moment, a fragment of up to 6 seconds can be made into a GIF.