My husband is a woodworker and he has an impressive amount of tools in the shop for cutting and chopping wood. From large table saws with impressive blades to tiny knives and files. Yet he can only use his two hands cut wood at any one time.
Likewise, I have an impressive amount of tea utensils for making tea. Yet, I can only use my two hands to make tea.
When we are doing temae, we should be concentrating on one thing at a time. Literally temae means the point in front of you. Handling the utensils should take all of our attention.
There is a proper way to pick up, carry, and put down each utensil. Each hand has its job to do and when it is not working, it has a proper place to be. Part of this is the mindfulness of keeping track of what we are doing. Another part is that using the proper hand to do something sets you up for something after. For example, if you pick up the bowl with your right hand you can immediately put it on your left palm. This also shows respect for the utensils and for the artists who created them.
If you are using two hands to handle or carry something, there is a greater attention to what you are handling. When my children were small and I asked them to use two hands, they paid much more attention what they were doing (less spilled milk). Likewise in the tea room, if you use two hands to handle something you are paying more attention to what you are doing.
Even in the mizuya, it is no place to let out attention lapse. Handle things with two hands. Pick them up and put them down properly. Don’t hand something directly to someone in the mizuya. Put it down in front of them, and let them pick it up. It is safer, and more attention is paid to what you are handling on both sides.
Last night, my husband asked me to hand him the TV remote. I remember picking it up with my right hand, transferring it to my left hand, turning it around like a chashaku with my right hand and placing it directly in front of him. He laughed, and told me only a tea person would have done that!