Why do beans squeak? We had some green beans in a chicken dish, and despite being well-cooked, they still squeaked against the teeth.   

Its not an unpleasent sensation, but it doesn't really blend with the other foods.

This has happened with both Green and Yellow beans that have been sliced but not "podded" like peas.

Not sure if it happens with broad beans, but definitely doesn't happen with tinned baked beans.  This squeak doesn't happen with cooked pea pods.

So what is special about beans that they can still squeak after cooking?
Is it something that can be cooked out of the beans?
From my experience, this is more likely to happen if the beans are cooked in a dry manner (eg as part of a pie filling, in a very thick sauce, or by sauteeing or baking) than when they are boiled - so par-boiling the beans before adding them might silence the squeak somewhat.

Also, the texture (and colour) of cooked grean beans is known to be somewhat pH dependent - if you are cooking them in a rather acidic sauce (eg one that has wine, vinegar, fruit juices ... added to it), you might also want to consider parcooking your beans separately.