に限って highlights one particular thing or person out of a group, with a nuance of 'of all things/people'. It often expresses regret, frustration, or a sense of irony when something negative occurs in that specific case. For example, if you lend your umbrella to a friend, and that day it rains heavily, you might say 'あの日に限って雨が降った' (Of all days, it had to rain on that day). The pattern emphasizes that the unlikely or unwanted thing happened precisely in that situation.

It can also be used without negative nuance to mean 'only' or 'particularly', but the majority of natural uses carry a tone of complaint or disappointment. In conversation, it is more common in spoken Japanese, but it also appears in writing.