To cause friction or worsen relations/situation by being blunt or tactless; to aggravate a situation.
会議で彼の率直な指摘が相手の角を立て、場が気まずくなった。
His blunt criticism at the meeting offended the other person and made the atmosphere awkward.
角を立てないようにやんわり注意したほうがいい。
It's better to warn them gently so as not to offend.
彼女のひと言で、これまでの努力が水の泡になり、関係に角を立ててしまった。
With her single remark, all the previous efforts were wasted and she ended up damaging the relationship.
To look angrily; to glare (often used in phrases like 'to have a sharp look in one's eyes').
彼はスタッフを叱って、目に角を立てて部屋を出て行った。
He scolded the staff, glared at them, and left the room.
注意された子どもは睨んで目に角を立てたが、すぐに泣き出した。
The scolded child glared angrily with a hard look, but then started crying.