Consider the unbiased concept class that contains every
teachable concept from $X$.
\[|C| = 2^{|X|}\]
Let the instances be defined by $n$ boolean features.
\[|X| = 2^n\] so \[|C| = 2^{2^n}\]
To learn this, the learner must use $H = C$.
We then have that
\[ m \geq \frac{1}{\epsilon}(2^n \ln 2 + \ln (\frac{1}{\delta}))
\]
so the number of examples needed is exponential in $n$ (well, since this is just an upper bound its not a proof of this fact, but the fact is true nonetheless).