sorry is something we all have to be at some point to learn true 'moral values' and people who are not sorry end up with self grandourous beliefs,narcissistic tenancies and hurt a lot of people
(and i know plenty of people like this, and plenty people who got like this due to never being asked to really be sorry )

if the person did this once, forgiving them will ease your mind thats true,
that is indeed a power they cant take away from you
but if they do it again, that will ease nothing.
and by doing it again they then are taking the power away from you

the person will have some problem that is making them internally angry and taking it out on you.
forgiving them every time only invites you to be hurt every time, invites them to never heal whatever problem they have and thats not helping anyone.

forgiveness is something that does have to be earned sometimes
you cant go about forgiving everyone for everything all the time,

look at society
there would be no punishment, no law, society would be pretty much anarchy.
people would do what ever they want with no fear of reprisal and confrontation
and those reprisals, the consequences are part of the reasons we dont all go around breaking the law willy nilly

is is really fair fair that you are a 'good person' per say who can be sorry when you hurt someone but be hurt by someone who doesn't care enough about you to be sorry for that?.

some people do things to hurt on purpose they dont need forgiveness, they need to be taught like a child stealing another's sweet that that kind of thing is wrong,

forgiveness like everything else in life has its time and place.

only you will know if this person deserves your forgiveness, and only you will know if they have done or are likely to do this again, and only you can know if forgiving them will make you happy.

to forgive someone who isnt sorry, although it depends on what has happened , what they did, why they did it etc,
i can say when i had to forgive someone for something that ruined my life, and who wasnt sorry
i found that realizing and accepting that the person wasnt really to blame was what helped heal me and helped me eventually forgive them.

forgive them by realizing that really internally they have a problem that causes them to act out,
that maybe it isnt their fault (if that is true, ie maybe they have a mental illness or a disability)
that maybe they are doing all they can to 'fix' themselves (as long as they really are)
if they accept they have a problem and ask for help its always easier to empathise and consider what they must be feeling and to forgive them

Another problem with not forgiving someone is that it gives them power over you. Think about it. You're upset, maybe even raging about what they did. Probably spending much more time and effort on it than it's worth. Point in fact, you are giving them power over you because you are choosing to devote time and effort to the problem.