You do not have to share with your neighbour if you do not want to. Well, your neighbour cannot build the fence on both of your properties, i.e., he cannot build it on the boarderline of your house and his house. He can only move back to his own backyard and build the fense on his own property. BTW, the goodlooking side of the fence (if the two sides do not look the same) has to face your backyard.
But you might get a very angry neighbour. Normally neighbours will share. Well, if you do not want to, definitely say no to your neighbour. The only risk is you might get an unfriendly neighbour... You might feel uncomfortable then...
Perhaps, legally, you don't have to share, but the question is, why not sharing the cost of the fence? It's nice to have a fence, and it is not fair to let your neighbour to cover the whole thing. You benefit from the fence, too.
I think you have to share. I came from Quebec and there is a law there saying that. I am not so sure about laws in Ottawa, you should check with the city first.
But either way, even if there is no law, why do you want to offend someone and become an as***le in your neighborhood for $800? (And that's a great price for you!) Believe me, if you don't share, there will be lots of fingers pointing behind you. After all, eveybody shares as far as I know.