I don't think there is a fallacy there. A difference of opinion, to be sure.
There is a world of difference between your ideations of killing yourself and being suicidal. Generally suicidal people plan their suicide. The plan will involve methods available to them. If a gun is in the house, maybe a gun. If not, a myriad of other methods are available, like electricity, suffocation, poison. If you are suicidal (and no need to confess that here) I hope that you are getting all the help you want and need to live the life you want to live.
A suicidal person doesn't need a gun to carry out the suicide. They will do what they need to do to accomplish their suicide.
A depressed person is not necessarily a suicidal person, also. Nor does that diagnosis abrogate their right to self-defense through legal means. The gun in the house is not an invitation to or a cause of suicide. There would be a lot more gun suicides if that were the case.
Ben, you shouldn't have a gun. Because you don't feel like it's a good idea for you. You made a choice, and a good one for you, and you can change your mind.
Other people also can and will make that choice wherever that choice is a legal one. Even if it's a bad idea for them.
Cigarrettes are still legal. You want to watch a slow suicide?