"... I found that when I ran outside, I went faster than on the treadmill. I don't know why... perhaps it's mental...."
That's interesting. I have a guess about that.
But, first, for a new runner, it is going to be much tougher to run outside than on a treadmill. It's more than the fact that the treadmill is pulling you along. It's because even on a totally flat course outside, you are constantly adjusting to small grades, stepping up sidewalks, off sidewalks. Over a six mile run, for example, those changes in grade add up to a much more strenuous workout.
Then, if as in your case, you are a cross-country runner, the workout is even more difficult. I run on hills and trails and that is so difficult compared to flat running, which is more difficult than treadmill running. That's why I smirk when my gym friends describe how they are running a six minute pace. Add 20% to that if you are doing exclusively treadmill running and then run outdoors.
On the other hand, if is very difficult for an outside runner, used to uneven trails, slopes, road cants etc., to adjust their gait to a treadmill. It feels odd because it's not really running in the same sense.