What is the danger in Thomas' writing down the instruction for thread dying in Gathering Blue?

The answer to this question can be found in Chapter Nine.
Having met Annabella for the first time, Kira feels completely bewildered by all that
she has to remember and very overwhelmed by what is expected of her. When she confesses
her feelings to Thomas, he comes up with a suggestion. He proposes that he writes the
information down for her so that she can have a record that he can read to her to help
her remember. Writing and reading are presented as important skills that only a few boys
are taught. Thomas, being one of these select few, is able to thus help
Kira.

Note the way that knowledge is presented as being
carefully controlled by the Council. It is "not permitted" for girls to learn how to
read and write, and thus it is potentially very dangerous for Thomas to record this
information and help Kira as Kira might learn how to read herself. Note Kira's response
to seeing Thomas write the words down:

readability="13">

When he read the word hollyhock
aloud with his finger on the word, she saw that it was long, with many lines
like tall stems. She turned her eyes away quickly so that she would not learn it, would
not be guilty of something clearly forbidden to her. But it made her smile, to see it,
to see how the pen formed the shapes and the shapes told a story of a
name.

Thus the danger lies in
the way that women are not allowed to learn how to read or write or have anything to do
with it. Discovery of what Thomas and Kira are doing could jeapordise Kira's
position.