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Listening in a multitalker scenario, we typically attend to a single talker through auditory selective attention. Inspired by human selective attention, we propose attentive training: a new training framework for talker-independent speaker extraction with an intrinsic selection mechanism. In the real world, multiple talkers very unlikely start speaking at the same time. Based on this observation, we train a deep neural network to create a representation for the first speaker and utilize it to extract or track that speaker from a multitalker noisy mixture. Experimental results demonstrate the superiority of attentive training over widely used permutation invariant training for talker-independent speaker extraction, especially in mismatched conditions in terms of the number of speakers, speaker interaction patterns, and the amount of speaker overlaps.