Traditionally (in the old days), with a twin engine aircraft the No 2 engine was started first. It may have started with the DC3 where the loading doors were on the left side of the fuselage as with most British and American types.
Again, traditionally in a four engine aircraft, No 3 was started first, followed by No 4 then No 2 then No 1. I have not heard of any specific reason why in the 737 No 2 is started first except it follows tradition.