Protest and anger practically always derives from hope, and the shouting out against injustice is always in the hope of those injustices being somewhat corrected and a little more justice established.

This quote is saying that protest and anger are often a result of wanting something better. People protest and show anger in order to draw attention to what they perceive as wrong, with the hope of making things better and establishing more justice. This can mean fighting for equal rights, better working conditions, or other forms of justice or fairness for those involved.