How do you measure and cut

I use both, but mainly rely on the ruler.

mat and ruler I am crazy need it perfect

Both, habit from how I was taught....

The ruler. Depending on the circumstances I sometimes line up the fabric on the mat. I agree that it's harder to get accurate cutting using the mat.

I was told to line it up on the mat but use the ruler so that's what I do.

I use the mat. I really don't think it matters as long as you consistently use one way or the other and not both.