My friend told me she forgot that my dad died!

You're right we all deal with things differently it doesnt mean their intentions arnt good

They could be going through a phase of amnesia. I went through it and it stayed for two years. I would always forget that my best friend is married, even though we'd speak to each other every week, and in mid conversation I would say something like "let's escape to the hills for a week" and she'd be like "Um... I'm married" and I'd feel embarrassed.
Amnesia can occur with depression and anxiety.
I hope both of you are doing okay.

That's minimum basic things one has to remember about their friends.
I find it unusual.