Eddie being Eddie away from home may not be the same Eddie AT home ...

I would guess Eddie's sarcastic or know it all behavior may have came from his mom or dad, and if it did they may regularly put him in his place / cut him off / limit his back talk - so at home he says little & away from home he says plenty ...

just my thoughts - anyone know more about Eddie's home life ? and why he's so out spoken ?

It's certainly plausible.

At work through the years, I mean decades, I've come to observe a number of people with a dual personality of sorts. Guys who, when I first met them were at work, were either/or aggressive alpha types, pontificating know-it-all types, wise-asses. Away from work, and to a much greater degree at home around their family, assumed a much more meek and compliant persona.

Imagine that. :)

Didn't Wally explain why Eddie is the way he is when he moved out and got that apartment and they got him to come back home?

A conversation was also had with his dad when they found out he was staying at home by himself after him and Wally got into it when Eddie was spending the nite over his house - I believe Beav asked him why he was friends with him..

Wally explained on a few occasions why Eddie acts the way he does, but I can't correctly remember what he said..

In the doll carriage episode, while Eddie and Wally were hunting for Beaver, Eddie told Wally he sympathized with Beaver because of something his dad made him do when he was small. And he told Wally he hadn't really told him anything since then.

I'd have to re-view the episode to remember exactly what it was, but it could have something to do with his later personality.

taken from the quotes page: maybe Eddie did have a tough home life +- (?)

Eddie Haskell) "Look Sam, if you can make the other guy feel like a goon first, then you don't feel like so much of a goon."
(Wally Cleaver) "I don't get that."
(Eddie Haskell) "Of course you don't. That's because you never went to kindergarten with a home permanent."

https://www.sitcomsonline.com/boards/showthread.php?t=378303&page=11

Yeah, that was it. He got Eddie a home permanent and sent him to school.

just my thoughts - anyone know more about Eddie's home life ? and why he's so out spoken ?

Likewise, "just my thoughts", but I always interpreted Eddie's strident nature on personal insecurity. By putting those around him on the spot, he places himself on "higher ground" by forcing them to either defend themselves, or simply surrender to his (self perceived) mastery of the moment?
I believe that Wally even explained Eddie's "creepiness" to Beaver along those lines once, in not as many words. Something along the lines of...so long as you're the one giving orders, then you're not the one taking orders.

Eddie would have made an ideal internet troll, in my estimation. YMMV.

^^^^
Eddie is insecure but is rather polite about putting others down.

He creates slight commotion(s) so others are too busy noticing his insecurites.