Pumping Lemma for Regular Language seems to Fail
The pumping lemma says that there exists a decomposition of $w$ to $xyz$ such that $y$ can be pumped.

It doesn't say that for all decompositions of $w$ to $xyz$, $y$ can be pumped.

In your example, a possible decomposition is: 

$x=a$

$y=bb$

$z=cd$