OP, I understand how you feel, even without the larger dynamic with your father. I've had to do things like give presentations or defend for advanced degrees (nerve-racking), and sometimes it bugs me when people say, "Oh, you'll do great!" It's not so much the words as the tone--I think it was GratefulMaria who first characterized it as "dismissive." I kind of wanted to say, "You don't know that! You don't know how nervous I am, how much work (or not) I've put into it, you just want to say something quick and move on to a new topic." Eh, whatever, you'll do great, now let's talk about my problems...
Obviously not everyone who says those words means it this way; I think a lot of them are sincere in trying to tell me something affirming and this is just a common way of expressing it, which happens to grate on me. It might be more a matter of personal preference than rude/not rude, though. For example, I would rather say to someone, encouragingly, "Good luck!" And someone who felt they'd worked really hard--"luck has nothing to do with it"--might take offense at that.