You shout at someone because you are angry with them or when insulting them.
You shout to someone who is far way because you want them to hear you.
With other verbs, as for instance, point, there are also different meanings and nuances.
If we insult someone, we use to or at with the same meaning. And I think that there is a certain nuance in “insult towards”: statements directed to denigrate, devalue or disregards people, organizations, institutions, etc.?
Someone could bring more light on this question?
José Manuel Rosón Bravo