There are a few reasons poker players might agree to crossbook, all competitive.
The first is simply for ego/in order to bet on who is the best player. If I think I’m better than player X at whatever game, I can offer to crossbook him. This means if I win more than him (which I believe I will), then he will owe me some multiple of the difference (could be 10%, could be 500%), and vice-versa. It’s a simple, pure form of betting on who is the stronger player.
However there’s no reason I have to be involved in the playing in order to crossbook. Say my friend is playing someone HU and I believe he is winning, while someone else believes he is NOT winning. Instead of arranging a challenge or endlessly flinging shit at each other, we could just agree to crossbook the results – if my friend wins, I win, if he loses, I lose. Now we can back our opinions with money instead of trading internet insults with each other. Hurray!
Lastly – there’s a practical reason two reputable players might want to crossbook. Especially in the current age of regulation, it can be difficult to get huge amounts of money onto poker sites in order to play nosebleed stakes. For this reason, it’s far easier to arrange the match say at $1/$2, or even at playmoney, agree the stakes privately and then simply send through whatever means at an agreed interval or once the match is finished. This saves liquidity problems, saves a few bucks on rake, but requires complete trust on both sides that the counterparty isn’t going to screw you if (WHEN! 😀 ) they lose.