The thing about being an MIB agent is that they are great liars. The recruits actually had a class that taught them how to lie like an expert. Not only did they learn to lie expertly, they also learned to decipher said masterful lie. Hence, a showdown between two MIB agents would be one intense affair.
Although all learn the same stuff, the way they soak it in is different. And as in any sector, they were people who excel at lying while some sucked. So, it wasn't enough to just learn it since the other person can always sound genuine to the point that you won't even doubt him even if you knew that every single word of his is a lie.
But the problem with Ponnappan and John is that both are self proclaimed experts at lying. Neither of them have ever been caught lying but they've caught plenty. So, both had an in-depth understanding about what a lie is, which made it really difficult for Ponnappan, who had the ball in his court.