Explaining why arrays are important for statisticians
If you are tutoring her, it is wonderful that you are trying to motivate the material in a practical way, but don't beat yourself up too much if you aren't that successful at persuading her. Some people just get themselves into a sort of myopic headspace where the only things that they need to learn are the exact operations that they will perform later on in their life.

However, it has been my experience that there is often something else going on in these situations. People aren't creating these excuses because of what will be practical in the future. They have no idea what the future holds. They actually create these utilitarian excuses simply because they don't find the topic intrinsically fun yet.

This also explains why you make no headway when you show her the utilitarian benefits; they aren't truly what is preventing her from diving in. Your best bet, then, is to show her why you think this whole field is amazing.

And if all else fails, go back to a utilitarian approach, but stick to the most direct reason: she needs this so that she will pass her class next semester.  That was a strong enough motivation for her to meet with you in the first place, so it should work out well enough to at least get you through the lessons.

Good luck!