The correct answer is A. discourteous.
A flippant remark is one that is made without serious thought or consideration, and is often dismissive or disrespectful. It is likely to annoy someone who is taking the matter seriously, as it shows a lack of respect for their feelings or concerns.
The other options are not as likely to cause annoyance. A bitter remark is one that is made out of anger or resentment, and is often hurtful or insulting. A humorous remark is one that is intended to be funny, and is not likely to cause offence unless it is in poor taste. A casual remark is one that is made without much thought or consideration, but is not necessarily dismissive or disrespectful.
In this case, the man is annoyed at the other person’s flippant remark because it shows a lack of respect for his feelings. The other person is not taking the matter seriously, and is making light of it. This is likely to make the man feel angry or frustrated.