Hi there.
Am wiring my unfinished basement with new wire, outlets, lights, etc. Only thing that was in it was a 14/3 spare. Split that and sent one-half to two single pole switches and 6 can lights total (4 can & 2 can). Used 14/2 AWG romex on everything. Changed breaker to a 15 amp ARC fault interrupter breaker per local code). Very careful not to let wires touch, everything tight, etc. Issue is every time I try to turn on light to see if I did the job right it pops the breaker. Thanks in advance

We don't know how you wired the basement but you obviously have done something incorrectly, wires crossed, grounded or connected wrong. If you used switch loops make sure the hot goes to the switch and not the neutral. You discovered the beauty of a breaker though, not having.to replace a fuse. Not sure of using a split neutral on an AFCI, they do not work with a GFCI.

Also double check you don't have the red and black touching anywhere (like on receptacle screws)

Only thing that was in it was a 14/3 spare.
Tell what that means, exactly.

A single pole Arc Fault circuit breaker will not work using a shared neutral.

OK,

You are confusing the world here. The term, "14/3" describes a three conductor cable that also has a bare ground wire inside the cable sheath.

This type of cable can easily be used in a multiwire circuit. I say this because it may be that the room was wired as part of a multwire circuit and you dismantled only half of the circuit.

Is that possible?

Even if local code allows it, you really should have the outlets and lighting on separate circuits. 15 amps for lighting and 20 amps for receptacles is pretty standard - each with a separate AFCI breaker. If ALL you are going to put on those few outlets are lamps, a stereo, etc then OK - 15 amps will do. But it may not be code-compliant.

Those arc fault breakers are SUPER sensitive. Your wiring needs to be pretty much perfect, well tightened-down and capped off with wire nuts / tape etc. if you are mingling new wiring with older stuff then there can easily be something going on that is getting in your way. I'd start with just the outlets, with a dedicate home run and get that up and running. Then do the lights next.

Good luck!