LED legs (the electrodes) are somewhat fragile. They will take a bit of abuse but will snap if you don't look after them. If you repeatedly waggle LED legs, they will usually snap just where they enter the LED itself, making the LED pretty much useless.
If you want to bend the legs on purpose, nip the legs tightly between finger and thumb halfway down their length. Then use your other hand to gently bend the leg. If you bend the legs here too much and they snap, you've still got enough leg left to solder onto.