Alita and Ido had a little fight since she wants to be a hunter warrior and he wants her to be his beautiful creation. He realizes that it is her life to live and not his, so she's free to make her own decisions.
Also, despite Ido not being the serial killer in the 1st chapter, he still enjoys killing and hunting criminals for his own sake, which is an interesting dynamic to his character. Alita also feels the same way when asked at the hunter registration why she wanted to become one. She said it was for her own sake. Now that she's been registered, what kind of trials will she face now? And at the end she faces the big dude who eats brains due to his endorphin addiction. She took out one of his arms, but he destroyed her whole body, which goes to show that she's not invincible despite being badass with the martial arts skills she's displayed so far. Hopefully Ido can save her and rebuild her body stronger.