I believe traditional masculine aggression was associated with wisdom and productive ambition and independence. It was not a method of expressing hostility and rage towards others.
Jewish aggression in males is meant to foster independence and the confidence that comes with labour and struggle against chaos and disorder to protect your community and your family. It is a mark of wisdom and dignity, not a filter that facilitates hate and wrath.
Bible aggression is not a status symbol derived from anger and combative self esteem, or a denigrating preset of competitive vanity. It is a charm key associated with divine advocacy and kindness. It deals with private self-control rather than extraneous rulership over offshoot connections.
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I'd say I mostly agree, but I think you are describing biblical masculinity in general, rather than aggression specifically. The media tends to represent masculinity as inherently violent and aggressive, but not in a virtuous way. There are countless Hollywood movies depicting conservative Christian men as abusive husbands and fathers, when masculinity in the Bible does not stand for that at all.
Additionally, you mentioned Judaism. I will warn you as a Christian that when you look into this "secular" media depicting these things, it is often actually Jewish. I have nothing against Jews, but that's just how it is.