In the Star Trek universe, and indeed on Vulcan, logic and emotion are opposites. One is a strength, and the other a diametrically opposed weakness.
It's just in Vulcan philosophy that logic and emotion are "opposites" and that emotion is "weakness." I think it's important to understand that this attitude doesn't really stem from any sort of philosophical underpinning so much as it is pragmatic and based on Vulcan physiology.
With much stronger and more violent emotions than humans, Vulcans had to devise an adaptation that would create enough peaceful public space to allow them to have any kind of society at all.
Emotions are a weakness for them. Making a fetish of logic and devising a philosophical underpinning for it is essential for them. It doesn't mean that it has much relevance to humans, Klingons or Andorians, whose physiology doesn't require it. So, for starters, Vulcan philosophy doesnt need to be assumed to be universal, and it doesn't need to be applicable to any of us.