'Out of' in this sense refers to the origin or the source, or the reason for your action. He offered his assistance not for financial gain, but OUT OF kindness. This is the original and more literal use of 'out of', meaning 'from'. It has nothing at all to do with the more modern and colloquial use, as in 'We're out of coffee' (i.e. having none left).

In this context, the phrase "out of ...something..." does not mean "having no more of ...something..." It means "from ... something...". Examples: "Out of his interest in learning the Chinese language, the student discovered an abiding passion for Chinese literature." "Out of his hatred for his ex-wife, the man became cold towards his children as well." "Out of compassion for her friend, the girl offered to pay for the friend's hospital bills." One way to think of this expression is to ask "where did y come from?" Answer "y came out of x".

or (just) as a matter of interest/(just) out of interest

It means JUST FOR CURIOSITY eg.: Out of interest, how long did it take you to write your first script?