A few years ago when I practised as a Mohel in London, I had such a case
and was instructed by Dayan Chanoch Ehrentreu, the Av Bet Din of the
London Bet Din, NOT to perform the Brit on Yom Kippur. I do not know
what his reason was, he simply said that we don't do it here in London.
I did not discuss the matter with him at the time, but perhaps the Dayan
was concerned about some of the matters mentioned below.
There are various other important considerations that must also be taken
into account when arranging a Brit on Shabbat or Yom Tov.
In many cases it will be quite certain that there will be a considerable
amount of Chillul Shabbat or Chillul Yom Tov (breaking the rules of
Shabbat or Yom Tov) by, for example, the non-religious members of the
family travelling by car or otherwise, to be present at the joyous
occasion. Or by people arriving, carrying gifts for the child.
If the Brit is to be carried out in Shul, as it probably would be on Yom
Kippur, there's the obvious problem of getting the baby there and back
home. He can't be wheeled in a pram, or driven in a car, by a Jew.
Although it's *very* important not to delay a Brit unless there's good
reason for it (and there are too many Mohelim who seem to perform Britot
only ever on Sundays!), a Mohel must be aware of all the implications of
performing one on a Holy Day.
There are some views that the Mitzvah of holding the Brit on Yom
Hashmini overrides all other considerations and others that one must
take into account all the ramifications of doing it on Shabbat or Yom
Tov and if it is known for sure that there will be much desecration of
the holiness of the day, it is better to postpone the Brit for the
Rabbi Geoffrey Shisler
Bournemouth Hebrew Congregation
Mitzvah Gedolah Liheyot Besimcha Tamid
It's a great Mitzvah to always be happy!