I would say because:
* If Scotland joins the EU then there must be customs checkpoints between England and Scotland. In the era of the modern nation state there has been no such formal border between the two countries. One can only imagine the number of business that rely on completely frictionless transfer of good across the border. At least in the case of Northern Ireland there is a recent historical precedent for border checkpoints (albeit one that's tied to painful memories). And yet look at how that's going.
* Scotland would be poorer. I can very much sympathize with Scots who don't like being ruled by English Tories (I'm English and I don't like it either!), but a lot more money flows from London to Scotland than in the other direction.
* The UK's nuclear deterrent would very likely be compromised. Some might say 'good riddance', but current world events are pretty nicely illustrating the strategic value of nuclear weapons. Scotland's GDP is about 6% of the UK's. It can't afford to fund its own defense. The SNP's plan for defense is either to pretend that it's not required, or just to assume that the remainder of the UK will continue to pay for it. On top of that, the armed forces employ a significant number of Scottish people (both directly and indirectly).
* The UK is already becoming a second-tier actor on the world stage. Split it up into smaller countries and the international influence of each will dwindle further.