<human>: My step mum is being very stubborn with the idea of Wi-Fi. I chew through quite a bit of data on my phone and my girlfriend comes over frequently and uses her phone and laptop a lot. All using up data. We recently got a new modem with Wi-Fi capability and my step mum refuses to let us set it up or give us the password. 

Her reasoning started as that it will let people hack into it. After my step mum realised that was false she moved onto the argument that we will use more internet. This isn't a problem as we are quite a wealthy family, I pay board that covers internet usage and most of all it wouldn't use that much download anyway.

This is becoming a problem due to the fact that now I am paying more on my phone plan to use data. (checking e-mails, facebook emssages and things of that nature.) When we have a perfectly good, easy to set up and use, secure wi-fi capabilities at our ready.

Overall she is just being stubborn and does not want to be wrong about this. How do I go about convincing her that wi-fi is not only a good idea but a more efficient one?

Could you distill the essence of the text into 1-3 sentences?
<bot>: Step-mum is too stubborn to let me set up wi-fi on our new modem for ridiculous reasons even though it is covered in the board money that I pay.