Animated UIImage in UITextView with TextKit
I think this behaviour is because the UITextView doesn't display the attachments using UIImageView subviews. When I observe the view hierarchy with and without the NSTextAttachments added to the UITextView, I don't see any new views (you can observe the view hierarchy using View Debugging in Xcode, or by saying [[[UIApplication sharedApplication] keyWindow] recursiveDescription]). Presumably, the UITextView just draws it's attachments directly.
That said, one way I can think of to include an animatable attachment is to create an animated UIImageView yourself as a subview of the UITextView, place it exactly where the NSLayoutManager places the NSTextAttachment, and scroll it whenever the UITextView scrolls. You can get the rectangle of the NSTextAttachment from the NSLayoutManager by calling boundingRectForGlyphRange:inTextContainer: (possibly in layoutManager:didCompleteLayoutForTextContainer:atEnd:).