Why wouldn't an arbitrageur who shorts an overpriced security, and longs a substitute company, break even? A Random Walk Down Wall Street (2015 11 ed, but an 2019 ed. is upcoming). p. 249 Top.

  Suppose irrational investors cause an oil company security to become overpriced relative to both its fundamental value and its peer oil companies. Arbitrageurs can simply sell the overpriced security short and buy a similar substitute oil company security. Thus, the arbitrageur is hedged in the sense that favorable or unfavorable events affecting the oil industry will influence both companies. A rise in the price of oil that makes the shorted security rise will make the arbitrageur’s long position rise as well.
  

Why wouldn’t this arbitrageur just break even, especially after transaction costs?
Case 1 of 2: The oil industry improves.
Then as written overhead, the substitute oil company's and shorted security's price rise. The former causes the arbitrageur  to gain money, and the latter  to lose money.
Case 2 of 2: It tumbles.
Then the substitute oil company's and shorted security's price drop. The former causes the arbitrageur  to lose money, and the latter  to gain  money.
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.