You have to keep in mind that the EU is much more than just a free trade area like NAFTA - but even with NAFTA, if for some reason one member state just up and left, it would be a nightmare for most companies in that member state who were doing regular business with companies in the remaining member states, and the other way around.
With the United Kingdom and the EU, it's much more complicated than that, because trade within the EU is so extensive, and currently so smooth, with only minimal border controls between the UK and e.g. France, and none at all between the UK and Ireland. This allows the UK, for instance, to be heavily dependent on suppliers in other EU member states for all sorts of products of which domestic production is quite limited - including many kinds of food, medicine and other essentials. British importers of such products don't currently need to keep large stocks, either, because they can just take daily deliveries from the continent. Of course there's also business going in the other direction.
None of that has to be a problem if the UK leaves the EU but remains in its customs union and 'single market', and even if the UK would eventually want to leave those, it would have time to realign its supply chains and arrange things so that a longer import procedure and perhaps higher cost from European suppliers can be dealt with - or perhaps the goods could be bought from elsewhere instead.
But the date of Brexit is end March 2019, in little more than four months. If by that time the UK will just leave the EU with no agreement on that kind of 'frictionless' free trade, it's going to be a mess both for the UK and for European companies/countries that do a lot of business with the UK. There are even serious suggestions that the UK needs to start building up massive stocks of such foodstuffs and medicines to avoid having shortages at the time of Brexit.
And that's just one aspect of it. There are many others, such as the position of Britons living on the continent, or other Europeans living in the UK. And again, possibly the biggest problem of all, the status of Northern Ireland.