Maybe there's more than just that one reason for how your mom feels. For instance:
1. Would this be the first gun to be stored in your house? Maybe she's just not comfortable with you having a pistol yet.
2. Do you have a safe, legal place to go shooting? How about gun safety courses, have you taken any?
3. Maybe your mom has liability and safety concerns besides whether the pistol would get stolen by burglars. Like whether or not it's going to be "out in the open" when she would rather not have it out in her house.
Maybe she has concerns about the potential use or handling of the gun in a manner that could make her (or another family member) legally liable in the event that somehow the government became involved in processing a complaint or if it were ever to be used for self defense purposes.
4. There may be plenty of other reasons that your mom has, and she might just be avoiding any mention of those reasons to not have to bicker with you over all of them. I think that your mom knows that a gun can fairly easily be safely stored and hidden from thieves, so could she be more worried about you than about the storage issue that you mentioned?
If storage is all that mom is really concerned about, then there should be a cereal box big enough (or laundry soap box, etc...), which can be placed in some inconspicuous place in your house that could very easily be used to safely store a locked (or disassembled) pistol or revolver and to help keep it hidden from burglars.