Complex sentence: The Soviet Union refused to accept this, either because it feared Kasparov would defect or because it thought Kasparov was the greater threat to reigning champion Anatoly Karpov; and their refusal would have meant that Kasparov forfeited his chance of challenging for the title.
Split into simpler sentences: The Soviet Union refused to accept this, either because it feared Kasparov would defect or because it thought Kasparov was the greater threat to reigning champion Anatoly Karpov. Their refusal would have meant that Kasparov forfeited his chance of challenging for the title.