How to stop my texts (iMessage) from showing on my Mac

Whenever I send or receive messages on my iPhone they show up on my MacBook also. I was wondering how I could get that to stop?

It used to be that my texts wouldn't show up, and I could message through my MacBook also but now its just annoying and I'd rather not have my siblings creeping through my messages by reading them on my laptop.

Disable it in iMessages Prefs/Accounts...

[Edit] Re-reading your question, you want to be able to send from iPhone & MacBook, but not have the MacBook show any conversations initiated from the phone?
Never tried that one, but perhaps by disabling one or more of the account number/email address options further down the same page.

I've always had conversations appear in both locations, Mac & phone, never seen it behave any differently, unless I was in some poor reception area.