Personally, and this is common in the UK, I do nt teach a horse to walk behind me, I like them to be shoulder to shoulder with me.
The reasons for this are that you can always see the horse's expression and anticipate what he is going to do next, if anything! A horse that is behind you and gets startled can and might slam into you from behind. If a horse does get startled then you stand a better chance of holding onto it if it is shoulder to shoulder. You can turn it in front of you or, if it comes into you, use your elbow to keep it out. Finally, I like a horse to be brave and not just follow. I have never had them assume they are my leader because they are slightly ahead of me.
If I have a horse that likes to come into my space when I am leading him then the point of a hoof pick against their shoulder keeps them over.
If the horse is behind you they will go around you, which I've had them do and have never been knocked down once from leading behind me. I don't allow them to get ahead of me...I am the leader and they follow me. Riding them has never been a problem at all by me leading like that.
I teach my horse to be brave by using a obstacle course which I built here in my arena and if they are nervous about something out riding I get them to go up closer to it and see that it's nothing to be afraid of.
I don't have to use a hoof pick to keep my horses out of my space, if they start to get in my space or ahead of me I take the lead line and swing it so they run into it.....
Everyone has their own way of doing things......