Idiom Request – Is There an Idiom for ‘Revealing a Secret Unintentionally’?

Actually, I can think of a few a colloquial expressions used in this situation, at least in my neck of the woods:

You want to be an English major and can't even explain what a verb is? You may as well hang it up.

...meaning "You better forget about becoming an English major and pick another subject."

An English major who can't explain what a verb is? Don't quit your day job.

...meaning "Don't quit your other job, because you won't make any money as an English major."

Some English major! You can't even explain what a verb is!

...meaning "And you claim to be an English major?..."

There's a saying (in American English, anyway) that is related but not quite exactly what you're looking for.

Money doesn't grow on trees.

That is, money has to come from something. It has to be earned. This same idea could be applied to inflation, still meaning that its value has to come from something, but the source could be gold reserves or GDP or something rather than labor hours.

If money did grow on trees, everyone would have lots of money, and therefore a unit of that money would be worth a lot less. The decrease in value is the general concept of inflation, although the "growing on trees" bit more directly relates to inflation caused by over-printing of currency and not other forms of value loss.