Absolutely agree with Buff. There were more elegant ways to handle this. The random outburst was the worst of them.

For example:
1) The guy's power has some other condition, like touching the opponent, but that method has more limited use and can be broken by will power.
2) The guy intentionally takes a hit from Izuku and then pretends to be seriously injured. Izuku might just accidentally let an "Are you alright?" spill out because he thinks he's already won.
3) Make the taunting more drawn out. The guy should insult far more than just one random acquaintance, like Izuku's mom for example.
4) The power works on interjections, so even an "Ah!" from Izuku will get him caught.

None of these are that difficult to think of, and they certainly aren't the best excuses either, but they are far better than what we saw here.