My mother-in-law talked to me, and as soon as I answered, her mother-in-law grabbed my words, with a loud voice. What does this mean?

Judging from your description, when your mother-in-law talks to you, as soon as you answer, her mother-in-law loudly grabs your words, which means: first, her mother-in-law should establish dignity in front of you and treat you as a junior who must obey; Second, when you answer, your mother-in-law finds that your answer conflicts with her expression, and you are denying her and making her angry; Third, your mother-in-law may be hard of hearing and can't hear your answer, so speak louder.