how is $p\to{\sim} p$ not a contradiction?? i understand that a contradiction is a proposition that Is always false, and in this case if p is false the implication is true, but in English this sentence sounds so contradictory: "if it's blue, then it's not blue" how does this even make sense?
 A: A naive person learns to recite the alphabet and thinks that means he's a great genius.
Another naive person learns to recite the alphabet and realizes that's a bare beginning of erudition and he must do a great deal more. He continues his schooling and goes on to become the author of the general theory of relativity.
Of the first naive person, one says: "If he's genius only because of that, then he's not a genius."
Thus "If $p$ then not $p.$"
This would be a contradiction only if $p$ were actually true.
A: 
"if it's blue, then it's not blue" how does this even make sense?

Let me rephrase:
"IF it's blue, then it's not blue"
OK, so it cannot be blue, for IF it were blue, THEN it's be both blue and not blue, and we'd have a problem.
OK, so it is not blue ... and note: if it is not blue ... then there is no problem at all!
So: if you ever have $p \to \neg p$, then we can conclude $\neg p$ ... and there is no contradiction.
Indeed: $p \to \neg p \Leftrightarrow \neg p$
But yes, many beginning students of logic get that one wrong. They believe $p \to \neg p \Leftrightarrow \bot$. No, we have $p \land \neg p \Leftrightarrow \bot$, but that's different. So, you're far from the only one! It's a classic, really.
A: The important thing is to realise that $q \to r$ is true already if $q$ is false. So also $p \to \lnot p$ is true if $p$ is false. This is contrary to the usage people expect in English or natural language.
