Why would Sirius need to be killed to keep a secret?

[pippin_999]

No: HPFGUIDX 163304

lone_white_werewolf:
> 
> Wouldn't Sirius's loyalty have been enough to prevent him revealing a
> secret?
>
Pippin:

>From what Dumbledore says in OOP, Voldemort thinks the balance of 
the prophecy contains information on how to destroy Harry. Sirius
behaves as if he believes that too, telling Harry to take the prophecy
and run, as if protecting the prophecy was worth every bit as much
as Harry's life.

So in his loyal effort to protect Harry, IMO Sirius inadvertently
revealed that he had been misled by disinformation that could only 
have reached him through one of Voldemort's agents. 

If Dumbledore realized that, he would trace the disinformation 
to its source, and Voldemort's spy in the Order would be revealed. 
Sirius had to be silenced before he could explain why he thought
the prophecy had to be protected.

So the prophecy establishes a motive for the murder of Sirius by
Voldemort's spy, Lupin's position between Harry and the platform
provides an opportunity, and a non-verbal spell provides the
method.  

It is of course difficult to believe that Lupin would turn against the
Order because he's such a powerful symbol of resistance -- but
alas, more symbol than reality if you examine his actions rather
than his words.

Pippin