N2
に限って
にかぎって
Particularly when, Those who, Only when
うちの子に限って、他の子に手を出すなんて考えられない。
I can't imagine that my child, in particular, would hit another kid.
Explanation
「に限って」 has 2 uses
1Just when
Of all times, trouble comes just then, said with a grumble: 「傘を持っていない日に限って雨が降る」 (it always rains the day I forget my umbrella). 「〜人に限って」: it's exactly that kind of person who…
昼寝をしている時に限って電話が鳴る。
Particularly when I am napping does the phone ring.
武くんと釣りに行く日に限って、いつも雨が降るんだよな。
Only on days when I go fishing with Takeshi-kun does it always rain.
2Not him, of all people
You're sure this person would never do something bad; a negative follows: 「うちの子に限って、そんなことはしない」 (my child, of all children, would never do that).
うちの子に限って、他の子に手を出すなんて考えられない。
I can't imagine that my child, in particular, would hit another kid.
彼に限って、こんな簡単なことでミスをする訳が無い。
There is no way that he, in particular, would make a mistake on something this simple.
Mixed up with
「だけ」: a neutral limit on the range.
「に限って」: not a neutral limit; it is either a complaint about bad luck or a firm bias in someone's favour.