@A31D31N I'm late to the part but....
Been a bit since I read this chapter so I may be wrong on some details, but I can understand why she would be hesitant for them to fight for a few reasons:
1 - Like you said she has 1 real point of reference for the power level of a hero. One thing she learned from the MC is that people from another world can be disaster levels of strong. She doesn't know this guy or how strong he actually is. On the Hero power scale is the MC a 10 while this guy is a 5 or is the MC a 5 while this guy is a 10? She has no real way of knowing. Unknown variables, and subsequently underestimating your opponents regardless of how strong you are, like this can be really fucking dangerous. You see a perfect example of this in the newer chapters of
. Hell MC has taught this lessen to most of his opponents.
2 - At this point I am pretty sure that Mage girl has seen the MC get hurt before, if not too badly. Due to this she knows he is not some invincible badass. If it can be hurt it can be killed.
3 - I don't think this is expressly stated but I'd say mage girl has seen enough to expect it: Collateral Damage. If these 2 go at it it isn't just some barroom brawl. It would be closer to Superman vs The Hulk if the Hero isn't instagibbed. even if you don't worry about damage to the surrounding buildings there would be a bunch of civilians in danger. The fact that the MC and The "Hero" don't step outside before they start getting ready to fight is really stupid. Granted MC might not care about collateral damage, but the Hero should.
That said in the end all of the above is pretty pointless since it was obvious neither girl wanted to go with Douche Hero. Even if it wasn't written on their face the conversation should have been:
DH - "Hey, the Goddess told me to party with you to fight the thing. Oh hey you look pretty and powerful Ms. Mage why don't you come too?"
FMCs (Both) - "Uh, no. We already have a good friend and ally to work with."
At this point it goes one of 2 ways:
Option 1:
DH - "Oh, well... shit. That sucks but whatever." Maybe with a "Lets at least stay in contact in case either groups need help or finds something really dangerous." added on.
Option 2:
DH - "Oh? Then why don't all of us join up and work to eliminate the Demon King?"
MC Party "Uh, no."
DH - *See option 1*
Instead DH seems to have decided to go the "Womenfolk don't have choices/opinions." That or the classic Chuuni route of "I'm the player they are all NPCs so they should obviously be listening/flocking to me.". Regardless I really hate this "Hero" and while I don't hope he dies I would like to see him lose a limb or two only to have the MC re-attach/regrow them. Love seeing cocky shitnuggets get put in their place. It is one reason why I fucking love The Misfit of Demon King Academy. Anos is one of the best at putting cocky dickwaffles in their place.