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two reasons;

Sony never intended the PSP to be capable of many of the things we take for granted on the internet, and while they have tried by adding browser, internet radio, rss feeds, out-dated Flash, etc..., the PSP just isn't a capable enough machine to handle YouTube.

And the most important reason is that they are not trying to make the PSP better any more. If it was able to play YouTube, it would only take away from sales of their newer portable device, the Vita.