Hey there, great question!
So Teddiursa benefits from EQ for 2 main reasons:
1) There are hordes, PvE Battles, etc. that benefit from EQ. In my guide, I linked the EV guide that I used where I calced against every horde to find a good setup
2) Teddiursa has night slash and belly drum as egg moves. For belly drum, you can use it for fun meme builds in a battle between friends. Night Slash is an excellent solo move that I personally use if I happen to encounter a shiny and want to defeat other pokemon in a horde
As for why Mild is better than attack:
- Teddiursa doesn't often take significant damage so it's better to make use of the fact that it can use a physically offensive and specially offensive moveset. It's also about getting the most out of the pokeyen you spend