"We must face the adversities of life with courage."
This implies (and is the case!) that life is not plain sailing - set-backs, traumas, calamities are part and parcel of the human condition and human experience.
"You will meet many adversities in your life."
I guess this is more from the "life should be a flower garden" school of living, and that people attending are the ones you will hear saying, "Nobody should have to go through this" The statement above might be the type of advice used in counselling the person to start seeing life through adult eyes.