Made me think back to why I switched to Linux. Easier for me as I came from OS/2, which faded away. But, to be honest, I was on OS/2 because I resented Microsoft for holdng back personal computing (by 4-5 years I reckon) by promoting the Windows 3.x/95/98/ME family (aka "Windows for DOS") rather than Windows NT, long after even entry level PCs could have run NT. Gates complained that he pulled MS out of the OS/2 partnership because IBM were holding progress back, and I believe him, so why then did he subsequently promote the abyssmal "Windows for DOS" for general use even into the new millenium?
But these are not good arguments for persuading others. Evangalising is out, even if it invokes recent MS misbehavour (like the ODF ISO affair). I think that the best persuasion is to give the impression that using Linux is a perfectly ordinary and sane thing to do.
A couple of years ago I gave a talk to my camera club and used Impress slideshow software on Linux. Before the start I deliberately had the Linux desktop visible on the screen - clearly not Windows - without comment before launching Impress - clearly not Powerpoint.
Then, just after the interval, before resuming my main topic, I said by the way just as a matter of interest you may have noticed that this Laptop is using Linux and a free version of power point called Impress. I said that I had prepared the slides and do all my photo work with The Gimp "It works with jpeg files same as Photoshop" (some other members already used Gimp on Windows). I recommended all these and said that it is all free, rock solid, and bullet-proof against viruses too.
The only thing is, I said, is that by installing Linux on my laptop, I had said goodbye to any guarantee or other support from PC World where I bought it. "If you see that as a problem, then Linux is not for you". But I added that my laptop was out of guarantee, and I would not trust support from PC World anyway.
A guy asked how "the Linux people" manage to do it for free. I said that Linux was mostly done by loose co-operation between big IT companies such IBM, Novell, HP, Google and Red Hat. Anyone but Microsoft. "It was their way of trying to get back at the MS monopoly". They made their money from support contracts, not by selling Linux. "They don't make money from me, but most of the servers on the Intenet run Linux, and probably your washing machine. That is where they get their income." These points seemed to make sense to my audience.
Thus I think that emphasising that its use is "normal", that the internet runs on it, its solidity, the commonality of file formats and its big company support, is the way to promote Linux.