Am i right for not forgiving him?

im not mad anymore, and at this point i really dont care what happens.
my step-dad who has been in my life for 15 years(im 16 now) and i've never been really close to him. we are always at each others throats about things and his relationship with my mom was never great. they were always fighting and threatening to split up but it never happened.
my step dad is also an alcoholic and he was always at a bar, like i only saw him once or twice in a week and whenever he was home he was drinking and just being a total ass hole.
then we find out that he was cheating on my mom with one of her friends that she introduced to him. my mom was devastated.
my parents are now separated and we are living in an apartment and he's living with his lover, he wont call her hs girlfriend so he's pretty much just using her,

i havent talked to him in almost 2 months and i dont think i will forgive him for this.
i want to know if im being a total brat about this.