Answer to this question is that there were two controversies between Natalya and Lomov .The first was about ownership of Oxen Meadows .They both believed that they were the rightful owners of the Oxen meadows.The second was about the superiority of their pet dogs Guess and Squeezer .
Their quarrel revealed about them is that both of them were underestimating each other and we're trying to prove that whatever they speak is true.