Would it be useful to learn how to drive a stick?

I enjoy to drive, and feel silly not knowing how to drive a vehicle with a manual transmission. Is there any particular reason I should learn, though? (For those non-USers here: automatics are the norm; a small minority drive with a manual transmission.) (For those USers here: manual transmissions are the norm in a lot of Europe.)

Also, everyone with a stick doesn’t want to teach me in their car because then they’re scared I’ll break their transmission—but they had to learn somewhere! How do I convince someone to teach me in their car?