The default YouTube app that comes with iOS was great back in 2007, but it hasn't seen a significant update in years and is lacking many features compared to the newer mobile YouTube website (m.youtube.com) that Google launched two years ago.
Reader seanm5 points out that you can stop iOS from launching the native YouTube app when you click on a YouTube link, and force it to use the superior YouTube mobile website instead. To do this, simply disable YouTube under Settings > General > Restrictions.
Once you've done that, all YouTube links you click on in an iOS browser will open YouTube's mobile website; the native YouTube app will also be hidden. If you decide you want to revert these changes and go back to using the YouTube app for those links, go to the Restrictions settings and toggle YouTube back on.