Why is learning DNF harder than learning CNF?
It's important to distinguish between $k$-CNF and CNF.  A $k$-CNF formula is a CNF formula where every clauses has at most $k$ literals; a CNF formula has no limit on the number of literals in each clause.

Both $k$-CNF and $k$-DNF are efficiently, properly PAC learnable, when $k$ is constant.  In contrast, as far as I am aware, it is not known whether CNF or DNF are efficiently, properly PAC learnable (no PAC-learning procedure is known for either).  So there is no asymmetry.

By "efficiently, properly PAC learnable", I mean that there is a polynomial-time algorithm for PAC learning, where the hypothesis space is the same as the concept space (e.g., given labelled instances from a $k$-CNF formula $\phi$, we want to find a $k$-CNF formula $\phi'$ that has low generalization error).

Since you haven't provided any references nor told us where you got the impression that $k$-DNF isn't PAC-learnable, it's hard to know what the exact source of your misconception might be.