Perhaps the most common thing I hear from people is this phrase!

And I can sympathise, I really can, as I started out as a very stiff person myself, some twenty years ago.  It is true that there are some dynamic styles of yoga where it is just not possible to keep up if you are very stiff.  Their philosophy seems to be that you either keep up or get out!  Rest assured that Iyengar yoga is not like that.   Iyengar teachers are trained to help stiff people.  In class I help stiffer students with adjustments so they can feel the benefit as much as the more flexible students.   As our aim is always the healthy action for your body, so whether or not you are flexible is kind of irrelevant!