Does Mikoto have a death wish? Based on the latest main manga chapter, i think she does.
Think about it, why does she want to fight Accelerator despite knowing that she will lose & die?
Simple, to redeem herself for what she has done, the creation and purpose of "The Sisters."
Even though she was just a child, she thought she was helping the Academy city scientists by giving her DNA, believing it would help them find a cure for
Duchenne muscular dystrophy but instead it wasn't.
At first she though they were going to use her clones as Military operatives but instead found something much worse. The only reasons they were ever created was to be slaughtered by the psychotic Accelerator so he could become a Level 6.
Feeling guilty for damming her Sister's who's only purpose in their lives was to be killed unmercifully and couldn't help them either(no matter how much she try to stop the experiment), this may explain why she constantly seeks to fight with Touma.
She doesn't want to fight with him and beat him, she wants to be punished by him for what she has done and failed to do. The reasons she choose Touma was because of two reasons:
1. She finally found an equal who can match with her.
2. Touma is a noble person who is willing to do the right thing, no matter the circumstances, a trait she greatly admires as most of the students she knows would rather mind their own business and not bother to help others.
In my view, she wants to be beaten by him (literally) because in her eyes, Touma is a Noble Knight (despite how unserious he is) and she feels only a noble person like him has the right to punish her for her Sins. Also her willingness to sacrifice her life to fight Accelerator is possibly to redeem herself and save the Sisters so they may live.
However, she's still a girl who's afraid of dying as we can see in chp 8 of Railgun but wants to do the right thing, even if it means losing her life, something she tries to do before Touma tries to stop her.
Writing all about this makes me feel kinda sad for her.
You views on this.