Depends on aircraft type but it goes back many years. Tradition, maybe? DC3, Convair 440, Friendship et al start No 2 engine first. Maybe because the captain usually starts the engine and with certain piston engines one became super-tuned to the progress of the start by the engine noise. Certainly in the R2800 engine of the Convair one listened carefully for a small drop in rpm that signified a mixture control/primer relationship. In other words you kept priming and ran on primer while opening the mixture control slowly and when the engine cut you released the primer switch and the engine than ran smoothly on mixture. Sounds complicated and it was, too. Then you closed the first officer's window to keep the noise of No 2 out and played the game again with No 1 engine. With some of the wartime four engine types the starting order was 3,4,2,1.
Useless info I know but a bit of history of interest to a few.