Continuing to talk after someone attempts to interrupt you prevents that person from being "the person who interrupted". They are spared from causing any social damage due to your assertiveness.
You have the responsibility to guarantee that you are acting with love and coherence. That is, you would consent to your colleagues treating you in the same way. Perhaps you are still wrong by continuing to talk. Perhaps you will still cause harm. But you can sleep well at night if you satisfy the guarantee.
This advice applies to the interrupter as well! Perhaps it is from a place of love that you interrupt. So sleep well too.