It won't for several reasons.
1. Bitcoin doesn't really work all that well. It certainly doesn't scale up. If the entire world, or even an entire small country, conducted all their daily transactions in Bitcoin, there wouldn't be enough room in the blocks to incorporate all those transactions. Bitcoin transactions take anywhere from ten minutes to over an hour to confirm, and that is way too long.
2. The current financial system stands a lot to lose by being replaced, and it won't just sit by and let itself be replaced. The smart financial institutions know they need to embrace cryptocurrency, which means that cryptocurrency will work alongside fiat money and current financial systems.
3. There are altcoins out there that work far better than Bitcoin and which can scale up. If any coin was going to replace fiat, it would be one or more of those altcoins. However, they won't replace fiat either, but will work alongside it.