Humans are social creatures, screaming is a natural response to summon backup to help deal with situations.
You're an adult male. You are the backup, so there are very few reasons why you should be screaming.
The way OP describes it, he feels distressed at the shrieking- this makes perfect sense. That feeling is his body telling him "WOMAN IN DANGER, GO SAVE HER, POTENTIAL MATE, PROTECT TRIBE!"
Like a baby's cry, a woman's scream just hits the brain in a spot that almost acts as a "button" that sends you into action, often before you even think it through.
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