Why are all finite languages regular? It is said that "All finite languages are regular". 

But the Pumping Lemma says that, 

if a language is regular 
one can find a 'large-enough' word w such that it can be decomposed into w = xyz such that FOR ALL i >= 0 the word with a pumped up y^i is also in the language. 

But doesn't that state that "every regular language is infinite" since one can always infinitely (i in N) pump the word up and it will be still in the language? 

So why are the finite languages regular and how are they fulfill the pumping lemma?
The pumping lemma states that if $L$ is a regular language, then there is an integer $p \geq 1$ (the "pumping length") such that every string $w$ in $L$ of length at least $p$ can be written as $w = xyz$ satisfying (1) $|y| \geq 1$, (2) $|xy| \leq p$ and (3) $(\forall n \geq 0)[xy^nz \in L]$.  (Source: https://en.wikipedia.org/wiki/Pumping_lemma_for_regular_languages#Formal_statement)

If $L$ is finite, then one can take the pumping length $p$ to be any integer greater than the length of any string in $L$.  The three conditions above would then be satisfied vacuously because there is no word in $L$ of length at least $p$.