You may just want to say you are sorry for what you feel you did wrong and let it go at that. At some point, they have to accept the apology and let the incident go. Your boyfriend's father did not react well to what you did so that needs to be considered as well. Flying into a rage over something insignificant then refusing to accept an apology is a bad sign. It means that the family could be dysfunctional and that can only cause you more pain. And if your boyfriend would leave you over such a small thing, then that does not bode well for his ability to stay in a relationship.
It sounds like you are blaming yourself for this incident. Taking all the blame is only going to hurt you further. Other people are not always right and they also do wrong things. It will help you to build your self esteem so you feel on more even ground and are able to see incidents like this as they are and not take the blame onto yourself.