He won't consider a 9mm or bigger to shoot with at the club as ammo is too expensive. So the .22 will be the only option. I just need to convince him. I don't want him to be unarmed, but he just believes a .22 is worthless. I don't think it is worthless.
Is 9mm really that much more costly than .38 Special? If cost wasn't a problem with .38, why is it an issue with 9mm? (Or .32, or .380, or 9x18?)
It appears that both you and your father want an easy answer for which no easy answer is available.
I truly believe that he will be better armed with my .22 pistol than with his .38 Special that only connects with 1 out of 5 shots. And that is in single action mode and really trying hard to shoot a group.
Better armed in what respect? Better able to punch holes in a paper target, or better able to protect himself against unexpected attacks, which are typically much closer? Here in the U.S., being attacked by dogs (Rottweilers, Pitt Bulls, German Shepherds) is arguably a greater threat than being attacked by humans -- although there is risk of both if you live in certain locales.
A .22 could be effective against either class of antagonist (human or canine) IF you had plenty of warning and are free to calmly sight and fire your weapon. But a human and a dog can travel 25-30 feet in just a few seconds. To further complicate matters, I don't think a .22 would have much effect on an aggravated Pitt Bull unless you got really lucky with a shot through an eye socket. Moving targets are hard to hit, even if you're an accomplished .22 shooter...
At our IDPA club, we demonstrated this at one of our IDPA matches several year ago, when we had a balloon mounted in the middle of an IDPA target, filling the center-mass circle; we had a target mover pulling the target across the rear of the indoor range.
A surprising number of folks, some of them quite accomplished shooters, simply couldn't pop the balloon. Success in hitting the balloon seemed more the result of "spray and pray" than the result of well-placed shots.
The problem, and it's a big one, is that most dog attacks and most human attacks don't come with a lot of warning, and tend to be UP CLOSE AND PERSONAL by the time a victim can bring a weapon to bear. With a dog attack, you may be on your back with a dog attached to your body before you can even fire your weapon.
Human attackers aren't likely to give you much warning, either.
I would argue that in that case, even a poorly shot .38 revolver or a Vector might be the better weapon of choice. Most guns used in self-defense situation aren't used at pistol-range distances.
If ammo is too expensive to practice with -- a cited deterrent to changing to something other than .22 -- your father has valued his life in a most flippant manner. If .38 special wasn't a cost limitation, maybe he needs to look at a DAO revolver, or having a gunsmith work on the .38's action so that it's more easily used.
(A gunsmith can do wonders with triggers on some guns.)
I'm currently saving up for a Glock. I just can't really make my mind up between a G34 or a G21.
Sell your father your Vector (he shoots it better than you), and get the Glock 34 or 35 -- depending on the availability of ammo. I loved a 34, had a 35, and now have a 23 and 38. The 38 is my favorite... but .45 GAP may be hard to get where you live.