If it were me, I’d have stopped the siman here. However, Shulchan Aruch added se’ifim 11-13, so AH includes them in one se’if, 16. A student should not remove his tefillin in front of his teacher, AH assumes because it means he will be bareheaded, however briefly [I could have imagined the answer is more about setting aside a mitzvah, even if it is common custom, is not to be done in full view of one’s teacher.]
The rule does not include a father, for reasons AH finds unclear [if the problem isn’t the lack of awe in being bareheaded, it could be that a father’s role is less focused on observance of mitzvot for the choice to take off tefillin to be less an implicit slap in the face]. And if one must choose between buying a mezuzah or tefillin, tefillin come first, although people obligated to show signs of mourning for other reasons—a menudeh, a person in the process of being disciplined by rabbinic authorities, or a metzora, someone suffering an isolating, Heaven-sent illness-- should not wear tefillin.
The siman teaches us about the frame of body and mind required for tefillin, all part of treating them with proper respect, some details of which appear in Scripture, some not.
