It's because stutterers tend to stutter less when they're acting out a role/character/personality or adopting a different mannerism of speaking. That's why some stutterers are more fluent when they're acting on stage/doing public speeches/talking to strangers than talking privately with a friend or family member. They have used a specific mannerism of speaking (which includes stuttering)with their long-time friend or family member for years and decades, and adopting a new mannerism of speaking or vocal personality seems almost like faking or lying to them. In order to sound "authentic" around their friends and family, they're unwilling to adopt new vocal tonalities, therefore unable to have more fluency in that situation. One technique I've used that increases my fluency is to emote when your speak, imbue every word that you speak with emotion (it can be passion, excitement, surprise, sadness, happiness, confusion, anger--whatever emotion is appropriate for the occasion). You can imitate the speaking style of the motivational speaker Tony Robbins. I've found that when I emote and animate when I speak, my stuttering goes down by a lot.