I’m saying it’s objectively not that complicated. EDM is any type of electronic dance music.

I personally disagree, and I know many others that do as well. I also don't feel like your take is invalid, despite being opposite of mine. Personally, I'd concede that the phrase "Electronic Dance Music" encompasses a ton of music and genres, but the specific use of "EDM" means something different to me and some others. I'm not making any statement on who is right or wrong, or that either view is completely incompatible with the other. You may have never heard anyone refer to it in the ways I or the other original commenter has, and that's okay... This is where I feel it's justified to call it "complicated" but you're welcome to describe it however you see fit.

House is dance music made electronically, therefore it’s EDM.

Again, I also don't fully agree. Despite the overwhelming vast majority of House music being Electronic-based, I have absolutely heard House music played live, with only analog instruments. I would not consider this a form of Electronic Dance Music. I would agree that most of it is Electronic Dance Music, though.