Rei's face at the end shows me why the "men" needed to be the one to deal the final blow. From the beginning he clearly has a holier than though view of himself where he thinks he can do no wrong and is being looked up to. Think about why he was convinced to have the party, it was to prove how great he was to the other guys for his "perfect" life as well as to have women swoon. It's why he had to dress up, why he can't take the blame and blames Rio and then Mahoro, and why learning the Rio was bragging shocks him because how could she do something he didn't know about, He can't be the fool but Haruto's final words destroyed the last of his ego by throwing him below all the people he looked down on.
I think we are going to see his crash out in the next chapter which I hope is why the "friends" were trying to defend him since they pretty much are reacting like they saw this a mile away.