Apologies

Elements of a Proper Apology: An apology is much, much more than "I'm sorry." That's just the beginning! You also need to tell the aggrieved party that (a) you recognize that what you did was wrong; (b) you feel bad about whatever wretched thing you did; and (c) you will genuinely do your best not to repeat said wretched behavior in the future. (Note: For particularly heinous crimes, you may have to do/say something extra in order to complete the apology; this may include discussing what the fuck you were thinking during the bout of bad behavior or doing something as a gesture of your sincere regret.)

If your apology does not include all of these elements, it will not come across as sincere. It is not sufficient to simply say you're sorry but neglect to change your behavior. Changing the harmful behavior that led to the need for the apology is the most crucial element here; if you exclude it, you may as well not issue the apology in the first place.

Insincere Apologies: If you're only apologizing because you want the offended party to like you again or you just want to smooth things over but don't actually understand what you did wrong, feel sorry about it, or plan to make sure it doesn't happen again, then you are delivering an insincere apology in bad faith. This is dishonest, condescending, and misleading, and it is not permitted.

Insincere apologies are false advertising, and you are pretending to be something you are not (nice, caring, sensitive, regretful, and most of all, unlikely to repeat the bad behavior). When you apologize, people assume that you are willing to do each step described above. That's the unspoken contractual agreement of an apology. If you aren't willing to commit to all the elements, not only are you misrepresenting your intentions, but you are also compounding your own bad behavior.