How do I convince my parents to get me a ps2 fat?

I'm looking for serious answers. I have a ps3, and I'm really grateful, but I got kind of disappointed when I saw that it said "This system is not compatible with and won't play ps2 games." In other words, when my parents bought me the ps3, I didn't know that it wasn't backwards compatible with ps2 games until I opened it. This is kind of disappointing considering that there were many games made for the ps2 that never will exist on the ps3 such as Midnight Club 3 Dub Edition and Harry Potter and the Chamber of Secrets in which you get to explore Diagon Alley. It's not that I don't like my ps3- I LOVE it, it's just that there are certain games that I always wanted to own and play that I never had the chance to. I want a ps2 fat simply because I like the look of it and the big air conditioning vents, but I also want it to be able to play ps2 games. I don't think it would be a good solution to get a WHOLE new backwards compatible ps3 just to play ps2 games, because I could always switch the cable for the TV between the ps2 and the ps3. How should I convince my parents to get a ps2 fat without being too pushy? Thanks.