Why do one way streets exist?

The existing roadway may be too narrow to accommodate two lanes (as for why is was so narrow in the first place, perhaps it was not intended to support parking but must for the sake of space). Or permitting traffic in a certain direction might clog up intersections somewhere else; traffic flow is a complicated thing.

Because they can.

Seriously, an advantage of one-way streets is that drivers do not have to watch for cars coming in the opposite direction, so in some cases accidents are reduced when streets with problem views are made to be one way. One way streets may be part of a system that helps traffic to flow smoothly, eliminates cross traffic turns, and makes it possible for someone to catch green lights all the way across town.

As the redoubtable Wikipedia says:

“Reasons for being one-way

* Street is too narrow for movement in both directions-in this case parking will only be allowed on one side of the street or not at all.
* To prevent drivers from cutting through residential streets rat runs to bypass traffic lights or other requirements to stop.
* Part of a one-way pair of two parallel one-way streets in opposite directions (a divided highway).
* For a proper functioning of a system of paid parking or other paid access.
* To calm traffic, especially if the street is historic.
* To eliminate turns that involve crossing in front of oncoming traffic.
* To reduce pollution from automobiles.”

Those details are worked out by the city planner(s) in order to determine what is going to allow the smoothest flow of traffic through the area.

When traffic is routed to one street in each direction, they can move twice as much traffic. I’m not sure how that works, but that’s the theory.