The first reason, in this particular retreat, is that we're trying to develop more of a Compassionate Intention, and if you get into the habit of reflecting while you are walking, it may be that you're not being aware of the beings that you may be stepping on. Or you may not be aware of the dangers that you are putting yourself into. When we reflect while we are walking, we may lose awareness of the present and our body, and that our body is moving, making it a little bit more dangerous to ourselves and other living beings.
We want to get you into the habit of settling your awareness into your body, becoming aware of the present, so that we can see what we are doing with our body, so we can put our compassionate intention into action. Then if you're in Bangkok, you're not reflecting about things as you're walking towards the street. Otherwise you may not be aware that there's a truck coming to the right or the left. You might be reflecting about death and yet with unawareness of your situation, you bring it to yourself more quickly!
Another reason is that we want you to get into the habit of settling into the present moment and your body, building this body awareness as a balance to reflection. Then in your busy life, you may find that between activities you are walking somewhere and your mind just settles down into your feet naturally. This is my experience over the many years where I was in a busy life, and I got up and started to walk. Then just through habit, beneficial habit, the mind settled down into the feet, and was able to drop some of the past worries, concerns, activities that I was pondering. As we drop more into the body we are able to see the hindrances more clearly. Then we can let go of the hindrances more quickly. We don't want to lose the ability of being able to learn how to recognize the hindrances and being able to let them go. We don't have to be reflecting all the time.
Another reason is it helps to balance the mind, giving a certain amount of tranquility. When we are doing a lot of Reflection meditation in the other postures, walking meditation can give more tranquility.