Why would Vegeta...

[SSJ2]

tell Nappa to take his scouter off? What harm would it do to have it on? They would have also been able to tell if there were any other reinforcements on the way..

 

[withheldforprivacy]

He had an eye fetish and wanted to see Nappa's eyes.

 

[Spiral-Force]

They initially saw Piccolo as the top dog of the planet, so any other reinforcements wouldn't mean much to them. Vegeta put it back on when it was made clear that Goku was their main guy and was on his way to help them; not because he thought he'd be a legitimate threat, but because he's Kakarot and Vegeta was dead set on making him suffer.

(Additionally, a scouter partially covers one's face, so taking it off provides more freedom.)

 

[Captain Cadaver]

Along with what Spiral-Force said, Nappa is the type of person to take the numbers placed before him as fact and overestimate his opponents based solely on them (eg. not thinking much of the Kienzan), so it was the best way for Vegeta to remove that flaw from him.

 

[SSJ2]

Fair enough in Nappa’s case, but Vegeta removing his own seems foolish. Confident or not, there is no harm in keeping it on.

 

[Spiral-Force]

How was it foolish in Vegeta's case? They were still slugs to him despite their ability to modify their battle power.

 

[Captain Cadaver]

^That, and given his shock at Goku being at 5k, it's clear he expected a post-training Goku to not even be a match for casual Nappa.

 

[Let's Go Fearless!]

Because he was arrogant as fuck and still is.

 

[Fantastische Hure]

Possible that shards could harm his eyes if they get destroyed during battle.

 

[Pocket-Gog~]

It's because the scouter looks so tacky, Vegeta has a developed fashion sense

 

[Fantastische Hure]

The scouter actually looked kewl on him.

 

[Pocket-Gog~]

The scouter actually looked kewl on him.

Maybe he didn't like it

 

[The_Authority]

It really looks like a distraction. Imagine fighting with one eye covered in colored glass that keeps beeping and displaying info in front of you. Now, if that info is correct, that's one thing. But if the info isn't even correct, all that scouter does, is impede vision.

 

[Warmmedown]

It's rose-tinted, so the confidence boost is worth it.

Thinking about that, it's impressive Vegeta was able to fight guys who presumably had powers over 6000 (Nappa's level, who I'd guess he trained with) while relying on his eyesight. Goku stopped relying on his eyesight at like 200BP, when he was fighting the likes of King Piccolo and then 23rd Tenshinhan.