On 2 Color Machine why is Cyan and Magenta printed first ?
Black and Yellow later.

I use to print black and yellow or black and cyan first.
Never did cyan and magenta first.

I always did K and Y first because M and C can be fine tuned on the last pass, that is to say, K and Y have a less effect on the final print

I've run Y and M the first pass and C and K the 2nd. Or if there were 2 dominant colors on the job that were very tight register I'd run whatever 2 colors those were mainly based of. We used to use color keys and read color density as well. I also found the Y and M would track less running back thru on the 2nd pass. Was a little more forgiving. Everyone has their way. So try a few and see what suits you the best.

back when i was running multiple pass 4/c process id try to match the sequence to the jobs requirements. if i were printing many flesh tones id opt to run magenta and yellow in the second pass. lots of blue sky and green grass would have cyan printing on the second pass. the most control over final product comes with the dominant colors on the last pass cause your looking at finished product

It's all about ink tacking which cause trapping....
4c press will start with Black, and 1 color press will start with Cyan,