When your opponent is correct to call (TOP)

[cmwck]

I was reading this example from Theory of Poker last night which got me thoroughly confused.

page 72:
"Let's say the odds are 5-to-1 against your opponent making a hand that beats yours. By betting $20 into a $150 pot, you are offering that player 8.5-to-1 odds ($170-to-$20), and so he is correct to call the $20."

It also goes on to say that it is correct for you to bet your better hand, even though you know he will call.

From this example I calculated each player's EV:

You bet $20. Your EV: (5*170 - 1*20) / 6 = +$138
He calls $20. His EV: (1*170 - 5*20) / 6 = +$12

Together both EVs sum to +$150, which happens to be the size of the pot. Now, we know that if someone has a positive EV, someone else must have a negative EV, and all EVs for all players must sum to 0. So, there is an EV of -$150 out there unaccounted for. But, we assume both players were heads up the whole time, so at any point in time their EVs must sum to 0. But their EVs sum to +$150. How can this be?

If it's +EV for you to bet with your better hand, and it's +EV for him to call with his drawing hand, it's an impossibility that both players will be making money in the same hand. By definition, heads up one player allways looses money to the other.