Comment by Natsu

The explanation of proofs I got in school was terrible. I had no idea that you could actually reduce everything to one of the applications of the axioms until I found metamath's proof explorer.

Of course, it's too much work for most normal purposes, and in school they accepted whatever random breakdown people used inconsistently and never explained why.

Actually understanding that it wasn't about convincing anyone so much as having a chain of reasoning going all the way back to the axioms was something of a revelation for me.