She's not 14, she's 15 (nearly 16) when that happens. And he's not a decade older than her, he's 20, so 5 years older than her. We're also talking about a Pseudo-Medieval World. Second of all, its FICTION.

GET. OVER. IT.

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Ok. You win.

You consider Alignment real when you have some grotesque rape monsters representing Alignment.
I exterminate flupmphs, pixies and demons (unless they are formed from souls of mortals whose choices turned them into demons that's OK) alike in name of Human Supremacy, because no being dumb enough to be stuck with racial Alignment, rather than Alignment caused by their choices do not deserve to exist - LG or CE, I don't give a shit. All dragons die chromies and metals alike.

So the main character of the show is called Goblin Slayer.  He has devoted his entire life to exterminating goblins.  That's all he does and all he cares about.  So how do you have a character like that as the main character without making him come across as just a psycho?  There has to be something about goblins that justifies this.  They have to be not just bad but inimical.  They have to be loathsome.  The first episode provides justification for why Goblin Slayer does what he does so he doesn't seem like a complete psycho later when he traps a whole tribe in a tree and burns them alive.   

Cow Girl's name is not unusual in the setting.  That's how characters are named in the series.  People don't call the female lead Priestess because they forgot her name.  That is her name.  That's the only name she gets.  Everyone is named like that.  The people in the adventuring party he comes across later are named High Elf Archer, Dwarf Shamam and Lizard Priest.  Those are the only names they get.  They are named like that because they are ttrpg characters.  This is made pretty clear when they talk about the gods rolling dice to determine their fate.