The reason I believe it is important to have an apologetic tone is to ensure you are communicating to the user that, though a mistake has been made and he is interacting with a machine or application in this case, you still respect his action and are humanizing the mistake.
To quote this article from UXMatters:
“You’re going to display your error message to a person, so write it
in the tone of voice you would use if you were telling the error
message to the person directly.”
I also recommend looking at this excellent article, Are You Saying “No” When You Could Be Saying “Yes” in Your Web Forms?:
Error messages seem like an unimportant and incredibly boring part of
crafting a user experience. But the tonality of error messages can
swing the experience around from an almost certain abandonment to a
conversion.
The article emphasizes that error messages should carry a positive tone and hence an apologetic response can help users quickly recover and not immediately become defensive about a mistake they might have made.
Writing error messages that carry a positive tone isn’t rocket
science. Just follow a few simple rules:
First, get rid of tech lingo such as “incompatible.” Most users won’t know what this means. Speak to them in their own language and
not the language of your developers. For example, “incompatible”
translates to “does not work together” in plain English.
Don’t use negative words
Clearly identify the error so the user knows what to correct.
Give the user a hint of how the problem can be solved.
Put the blame on yourself, not on the user.
I also recommend looking at
The Effect of Apologetic Error Messages and Mood States on Computer Users’ Self-appraisal of Performance for a study which analyzed the impact of using apologetic error messages on user mood states and how human-like apologetic tones are effective in computer interfaces. To quote an extract from the article
In HHI, apologies are generally used to express regret (Leech, 1983;
Schlenker andDarby, 1981) or to alleviate individuals’ anger caused
from their disapproval of others’ action.In other words, apologies
mitigate frustration and anger when attempted interactions
fail.Similarly, Nielsen (1998) argues that error messages responding
to the computer user’s action should include a simple apologetic
statement when the reason for the error is the limitation of the
computer interface to perform the intended task. Tzeng (2006)
conducted a study investigating users’ perceptions of online systems
containing three different error messages,each of which includes
different politeness strategies. In the study, firstly users’
politeness orientations were elicited and then participants were asked
to interact with websites including pre-determined problems. When
users encountered problems, the system provided certain error messages
representing one positive politeness strategy (i.e. joke), one
negative politeness strategy (i.e. a simple apology), and a mechanical
message for the error (i.e. the page is temporarily unavailable). The
findings of the study showed that users who deal with social events
with polite expressions preferred to receive apologetic messages
significantly more than mechanical or joke messages, and they
preferred apologetic messages significantly more than those messages
that are less oriented to polite expressions.
The article also calls out how an apologetic tone as opposed to a negative tone impacts the perception that users of them selves and how a positive apologetic perception can help in enhancing positive performance
De Laere, Lundgren, and Howe(1998) compared human-like versus
machine-like interaction styles of computer interfaces.They did not
observe a significant difference between the different styles in terms
of users’self-appraisals. The findings of the study also demonstrated
that negative feedback affects the self-perceptions of the
participants differently than positive feedback.
Tzeng (2004) examined whether apologetic feedback affects users’
performance perception in the computerized environment. This study
suggested that users may not expect computers to be polite, but
apologetic statements made the subjects feel better about their
interactions with the program.
The research paper Computer Apology: The Effect of the Apologetic Feedback on Users in Computerized Environment also calls out why apologetic negative feedback ties into user experience from a social aspect
The use of apologetic statements with an error message contributes
the human-computer interaction. If we consider that the main aim of
the user centered design is to create an environment for users in
which they feel themselves comfortable, use of apologetic statements
in the user interface design become a very important issue. Moreover,
in human-human interaction, one of the more important, may be the
most, issues is to behave in a respectful manner. In most of the
societies when a person does not behave in a respectful manner or
makes a mistake towards the other person, apologizing is the
traditional and the most effective way in order to overcome the
problem. Similarly, this study shows that most of the subjects
thought that apologetic feedbacks do not seem awkward to them and
95% of them receiving apologetic feedback felt that apologetic
feedback seemed sensitive to them. Here, it seems that subjects find
it interesting to confront with respectful behavior such as
apologizing when they encounter an error caused by computers’
inability as if they encounter a problem in human interaction. The
findings of this study indicate that representing the affective state
of a person in the interface design is very important in
human-computer interaction because people are more sympathetic to see
emotional aspects in the interface such as, sensitivity, respect, and
feeling of humanity. Therefore, these results might be used as
evidence for the claim that computers’ offering apologetic statements
to the users can substantiate the idea of real user centered design.
On the flip side Microsoft recommends using sorry or an apologetic tone only when a serious error has occurred:
Use the word “sorry” only in error messages that result in serious
problems for the user (for example, data loss or inability to use the
computer). Don’t apologize if the issue occurred during the normal
functioning of the program (for example, if the user needs to wait for
a network connection to be found).