If you have a target active, while holding L2/R2 and you press L1/R1, you will "cycle" target, so switch, this happens to new players when they have to switch crosshotbar by holding R1 then press up, down, circle..etc... or by simply switching crosshotbar by pressing R1

You may also be pressing, left or right without holding L2/R2, by doing so you switch targets

I think this is your case, if it is not..i can tthink of any other things atm