The right wing in one party and the left wing in the other are vying to take control of the country. The EU debate is a useful vehicle to fight out this battle.
And luckily neither can succeed without taking the middle ground
Which I think is why brexit is so difficult. There is, as Leo explains, no middle ground. Between a rock and a hard place as the Yanks say.
Doesn't mean we cannot make a success which ever way we go. Or indeed if the EU collapses it may be seen as a success even if it is a disaster.
But like any major change it will be painful for many