Asura.Artemyse said:
I've done what you said also, but what I said is directly from what SE said on the Loadstone.
http://lodestone.finalfantasyxiv.com/pl/topics/detail?id=5542db352bb764087916b9d9200acf78650edf81
Read Q & A #4
Lodestone said:
Q. I am able to choose between using my main hand or off hand tool when beginning a synthesis. What is the difference?
A. Main hand and off hand tools have varying characteristics which manifest themselves in different ways when a high-quality result is achieved while synthesizing. There are many possible outcomes. For instance, a successful synthesis with a main hand tool may result in a +1 or +2 item, while the result obtained with an off hand tool may be a higher yield of regular quality items.
Key word bolded.. They didn't say all craft's (or any craft) main hand will result in +1 or +2 items, they said it
may do so. They were just giving an example, not a specific answer.