This is a good question. There are several places where gender comes into play in these chapters.
First, Atticus explains to Scout in chapter 19 that Tom was in a grave predicament. When Mayella came onto him, he would not dare touch her. If he did, he would be guilty immediately on account of the racism in Maycomb. So, he had to do the next best thing, which was to run. But this would be a sign of his guilt. This shows that a white woman, no matter how much at fault, had power over a black man. Here is the dialogue:
It occurred to me that in their own way, Tom Robinson’s manners were as good as Atticus’s. Until my father explained it to me later, I did not understand the subtlety of Tom’s predicament: he would not have dared strike a white woman under any circumstances and expect to live long, so he took the first opportunity to run—a sure sign of guilt.
During the trial, Tom's great fault was to feel sorry for a white woman. The people took this as a sign of his arrogance. This shows that hierarchy once again. In Maycomb and elsewhere at the time, white women were above black men, even the best of them. Here is what the text says:
“And so a quiet, respectable, humble Negro who had the unmitigated temerity to ‘feel sorry’ for a white woman has had to put his word against two white people’s."
If you tease out the logic here, there is a lot to say.