Fickleness is a trait of being likely to change, especially when it comes to loyalty or feelings. Your dog's fickleness might mean she loves you best today, but your brother will be her favorite tomorrow.
A person's fickleness tends to make them unreliable — they're not someone you can count on, since they are so inconsistent. You can also use this noun for anything that changes unpredictably, like the climate: "The weather's fickleness in September meant they decided to have the party indoors." Fickleness comes from the adjective fickle and its Old English root meaning "cunning or tricky."