Step-by-step explanation:
1a) When they call the Montagues "dogs," they are looking down upon them with scorn. They're not talking about cute little dogs that are pets. The two families see each other as the lowest of the low.
1b) Tybalt is far more violent. He openly threatens him: "Turn thee Benvolio! look upon thy death." Benvolio replies by saying he just wants to "keep the peace." Shakespeare is establishing a precedent for the comparison of their characters, and we'll see more of Tybalt's fiery spirit later.
1c) Capulet's wife asks her husband "Why call you for a sword?" and Montague's wife commands hers "Thou shalt not stir one foot to seek a foe." Clearly, the two women don't want any more strife between their families. They are wise enough to know that the conflict could end in death.