I heard that using "had better" sounds arrogant. Anyway, how about using "better".
e.g.) You had better go back home. arrogant.
You better go back home today. is it arrogant?

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It sounds more urgent. Urgency can sound arrogant if it's misplaced.

e.g. The sun is setting, and your friend has to walk home where there aren't a lot of streetlights, and doesn't have a flashlight to get home. Maybe they're procrastinating a little bit more than they should.

"You had better get home before it gets dark."

This doesn't sound arrogant, it's the smart thing to do. Sure there are other ways to put it that aren't as direct, but it could be dangerous to walk home in the dark.

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But, it can definitely sound arrogant if you make it falsely urgent, or put yourself in a place of authority that you shouldn't be.

e.g. You and your friends are hanging out and someone says they need to head out and you reply

"You had better go back home."

At first I'd bet they would think you are joking. This is something my close friends and I do as somewhat of a parody, an "over-confident gag".

"Yeah, you better..." or

"That's right you're going to..."

Usually accompanied by a very over-the-top voice. If it were with a serious tone and intent, it would probably be pretty insulting given the scenario.