We must be aware that these anti-love characteristics in 1 Cor. 13:4-5 begin in the heart and as the heart speaks self-exalting things to ourselves, we swell up with pride until what is inside spills out of our mouths.  Thus the main goal is NOT to make sure you don’t sound like a braggart to others, but that you don’t coddle self-exalting thoughts in your hearts about anything in your life.  You may be top dog at work or you may be extremely gifted at a skill or sport or maybe you have a personality that others gravitate towards.  No matter what the cause, what do you do with the praise and recognition you receive from others?  Rehearsing that praise in your minds and allowing it to make you feel good about yourself will cultivate pride in your life.  Then you have a hard time receiving a rebuke from those who know you, because in your mind, these other people who are praising you are much more in tune to the true you, so for others to point our faults is an indictment on them for not recognizing that they are standing in front of true greatness!
So these two words describing pride are what essentially Paul was rebuking in the first 3 verse of 1st Corinthians 13 because they pollute and spoil even things which are good, like spiritual gifts, like the knowledge of God and like giving to benefit others.