Children are the property of their fathers. Preserving the value of that property through preserving the virginal status of females is the responsibility of both sons and daughters. For a son to have sex with the daughter of another man, both the daughter and that boy have committed a property crime against the girls father. If she gets pregnant, he will never be able to get as big of a dowry when he sells her into marriage.

At least, that's where the idea of tying sexuality to economic considerations like 'responsibility' and phrases like 'saving yourself' come from.

Totally impossible for a term like "responsible" to have multiple meanings.

Obviously people mean the economic term. Couldn't possibly be the everyday meaning.

You mean bride price, dowry is what the bride's family gives