"No, baby, no, you may not go, For the dogs are fierce and wild, And clubs and hoses, guns and jails Aren't good for a little child.
The mother thinks that it is just too dangerous downtown.
Why? Because many of these marches were broken up by the police. The mother mentions the dogs, clubs, hoses, and guns, which were often used to subdue people marching in these protests—even if the protestors weren't being violent. They are also symbols of the violence that many African Americans of this time had to endure.
Police also jailed many of the protestors. Even Dr. King was taken to jail during a non-violent protest earlier in 1963. In fact, he wrote one of his most famous letters, "Letter from Birmingham Jail," while he was in his cell.
But why would dogs or guns be a risk for a child? Surely they wouldn't be getting into any trouble downtown?
Well, the mother's fear shows that anyone who participates in the marches would be at risk of police brutality, even if they were as innocent as a child.
And he's also being historically accurate: there were plenty of children attending these marches, and several images depict them facing police brutality as a result.
The mother doesn't want her daughter taking any risks, so she forbids her from going to the march.