Someone else had updated their iPhone on my computer in the past, and now every time I open iTunes, it automatically shows their phone in the Device column and not my own (when neither their phone nor my phone is plugged into the computer). How can I stop this from happening? How can I make my friend's phone disappear from my iTunes completely? I have already wiped iTunes off my computer, and reinstalled it, but this problem still occurs.
Eject the device.
It sounds like your friend selected the 'sync this iPhone via Wi-Fi'-option. Does your friend's iPhone always appear in your iTunes or does it only appear when your friend's iPhone is connected to the same Wi-Fi network as your computer? If the latter is true your problem will be solved easily.
Click on your friend's iPhone in the left column in iTunes > If not already selected, select the general tab > Scroll down. Among the options listed you should see a option called something like "sync this iPhone via Wi-Fi". (My iTunes is set in a different language.) Uncheck the checkbox next to this option. > In the lower right corner of iTunes click on "Apply" and then on "synchronize". > When your friends iPhone is done syncing, you can eject your friend's iPhone in the left column in iTunes.
Warning: Depending on the syncing settings and options some of the data on his iPhone (music, apps,...) might get replaced with your music, apps, etc. in the process. So be careful there.
I would try going to iTunes > Preferences > Devices, and deleting any backups of the other phone from there.