Why? Because the routes are created by each protocol specified by each routing protocol in their own unique way which is not understood by other routing protocols. But thankfully you can configure 'redistribution' which will convert an OSPF route into a BGP route and convert a BGP route into an OSPF route. But the catch is you need to manually specify what the route is worth in the protocol you are redistributing to (e.g. if you're redistributing a BGP route into OSPF, will these routes be type 1 or 2? Well you need to tell the router that).
To answer your last question: You have to redistribute the route both ways.
Routing protocols have their own completely unique ways of measuring and comparing one route from another.
OSPF will measure routes based on the 'cost' to get to that remote route. BGP uses a whole different world of measuring and comparing routes, it uses things like how many Autonomous Systems (AS) are between itself and the remote route, the local preference, weight, whether the route was internal or external BGP, and etc and so forth.
If you want a BGP network to process OSPF routes, you need to convert those OSPF routes into BGP routes by 'redistribution'. And vice versa. If you didn't do that each protocol would have no idea what the opposite routing protocol's routes are worth or mean.
Try spending US dollar bills in Europe, sure they can see that it's money but they won't do anything with it until you convert it first into something they use and understand.
