Can I add a light fixture to an existing circuit but with its own switch?
Assuming the Fixtures are all on a 15AMP Circuit and using 14/2 wire.

The Complexity would depend on how the Switch was wired.   Power to the Switch, Switch Leg to the Fixture, or Power to the Fixture and Switch leg down and back.   If you have the Power at the Fixture then you won't have a Neutral at the Switch.  If its a newer house you should have a White wire in the Switch box that is just passing though and only connected to other white wires. 

If you have a Neutral in the Switch box, and If you have Access to Drop a second 14/2 from the new Fixture to the existing switch then sure.   You just Connect up all the Neutrals, then get a Switch like this 

Connect the Existing Hot Switch leg to one switch and your new Fixture's hot switch leg to the other switch. 

If there is no Neutral then  you have two options:

Option #1 Branch the Incoming Power from the Existing Fixture down using a 14/2 to the Existing Switch. Then You will have a new HOT and Neutral in the Box. Then add a second 14/2 up to the new Fixture. Use the same Switch as above though remove the interlock between them so you can feed separate HOT feeds. 

Option #2 is to do as they did and branch from existing Fixture to new Fixture.   Take the incoming hot at the old fixture, Tap off it to the new fixture.   You will need a 14/2 down to the switch in this case too. You connect the HOT from the existing Fixture to the HOT of the line you ran to the switch box. Then use the same switch though you are going to remove the interlock between them so you have an incoming hot for each fixture. Then use the white wire after its labeled to provide power back up to the Fixture.