"If they were lukewarm about it, why take it to the Supreme Court?"
Oh, no, not again!
Read the very first part of Article 50. Go on, Google it now and read it. Look, seeing as you probably CBA, here's the link: http://www.europarl.europa.eu/RegData/etudes/BRIE/2016/577971/EPRS_BRI(2016)577971_EN.pdf Now read it.
Still CBA? Here's the relevant passage: 1. Any Member State may decide to withdraw from the Union in accordance with its own constitutional requirements.
Now you tell me, what are the UK's constitutional requirements for this - and what's your authority for that?
You see, it's unprecedented. HMG think Royal Prerogative provides the requirement. But we've spent over a third of a millennium - that's right, right back to the Civil Wars in the 1640s - establishing something called the sovereignty of Parliament. Some people think that means Parliament's decision is the constitutional requirement.
The way to resolve this, the only way, is to get the decision of the courts. ATM the decision of the High Court is in favour of Parliament. HMG have appealed to the Supreme Court where it will be decided once and for all.
Whilst my own view is in favour of Parliament making the decision I still think it right that the matter should have gone to the Supreme Court because we really do need a definitive decision.
Consider, for instance, the situation if Article 50 was invoked irrespective of whether it was by Her Majesty May using the Royal Prerogative or Parliament passing an Act without a ruling. Brexit will inevitably cause expense - redundancies etc - for those corporations who have set up in the UK because it gave them an EU base. Suppose one or several of them were then to demand a Judicial Review on the basis that the constitutional requirement wasn't met. Can you imagine the chaos it would cause?
Do you now see why it's important to get this settled now irrespective of whether you think Brexit is the best thing since sliced bread or a mistake that's going to cost swathes of its supporters their livelihoods?