Why wouldn't an arbitrageur who shorts an overpriced security, and longs a substitute company, break even?
Yes, you've understood half the reason for taking the joint position: if sector-wide movements occur, then the position stays neutral: i.e. it is insulated from those movements.

It's not sector-wide movements that this position is trying to profit from. So it's wise to insulate the position from those movements.

What this position is trying to profit from, is the relative over-pricing of the shorted-security, and the relative under-pricing of its competitor. If the arbitrageurs are correct, and can stay solvent long enough, then each of their two positions will make a profit when the shorted security drops in price, and the held security rises in price.