I am pretty sure that it comes from when Jesus sent people out two at a time. which if it was good enough for Jesus it was good enough for people in TWI because its in the Word.
One time I went with a partner who was afraid to talk and I kept telling him that he was going to do the next one but then he wouldn't talk again. So I would talk and tell them about TWI. He kept chickening out. It was the fear I think. One time I told him that he was going to talk and I was going to keep my mouth shut no matter what. When the man answered his door and said can I help you, I kept my mouth shut but so did my partner. The man kept loking back and forth at us. I was kind of smiling but my partner was looking real scaird. Then the man said Well? What do you want? And I wanted to talk real bad because it was getting real weird but I didn't talk, and my partner was still looking real scared. Then the man finally said real loud, what do you want? Finally my partner began to speak and he went and blurted out, Do you live around here? The man was really laughing when he closed the door.
Maybe witnessing together is good so you can pray for eachother to not be so afraid. But it sounds like maybe it wasn't that way lately in TWI. It seems as if things in TWI got weird