Some context:

My dad and I have always gotten along pretty well. But there are times when he'll just start spreading misinformation to members of my family, or he'll be completely wrong about things that are easily googled when talking to his coworkers.

For example, if my sister is working on stuff for school like math homework for example, he'll start doing the problem with her and halfway through he'll make an error or explain something to her that's not correct and then blame the textbook and say things like "well if that's what the textbook says then the textbook is wrong," or "well if they're teaching you that in school then your teachers are not doing their jobs." It's really frustrating to me because even when I'm polite about it and I tell him "hey, that's what the teachers are teaching her in school, the textbooks aren't wrong and you're starting to confuse her" and I go to help my sister he gets upset with me and starts saying things like "well you're always right" or "forgive me for being so damn stupid." 

He also tends to make up statistics to make him sound like he knows what he's talking about and it makes me worry about him hanging out with his coworkers (whom are half his age) and just being dead wrong about some things. I love my father to death and the last thing that I want to happen to him is to be made fun of or thought stupid by his coworkers.

 Part of me things that I might be coming off as condescending when I correct him, but I never do it in public or in front of people (apart from my sister or my mother) because I don't want to embarrass him or make him feel like he's dumb. Keep in mind that my dad is a genius when it comes to extrusion and factory work, he' been with the same company for years and he's really good at his job.

I'd like to point out that I am by no means a superbly intelligent person myself, and my goal isn't to demean or belittle my dad.

If it turns out that I have been an asshole I definitely want to apologize to him, and probably will anyway.

Am I the asshole?

TLDR: My dad corrects my sister on her homework and is misinforming her so I correct him and he gets upset with me and says that he's always wrong and that he must be such an idiot (in a condescending tone). Am I the asshole for correcting my dad?

Thanks.