A lot of things happen for historical reasons, in the old days it was common to start the right engine of a propellor aircraft first in order to board passengers, for lack of any better reasons this policy was carried over into the first jets.
Taken from a Piedmont B737 Manual dated 1978.
The No2 engine will normally be started first to facilitate last minute passenger loading or retraction of the forward or aft stairs
But as others have pointed out, there is no limitation forcing you to do so.
Mutt.