A girl at work brought in her two bettas one day. They were both in tiny, unheated containers, but even though they were lethargic from the cold, they were brimming with personality and each had very individual quirks. I was charmed by how interactive they were. I grew up with a 20G tank of schooling fish, and while they were pretty to look at, I didn't really think they had a pet-like quality, but bettas do. They recognize faces, they understand routines, and they can be trained to do certain behaviors on command just like a dog. They are surprisingly intelligent and endearing. Their aggressive, solitary nature means that you are the center of their world, and the fact that their world is so small means that they utterly depend on you for everything. It's nice to feel needed, even if it's "just a fish" doing the needing.
One big drawback is widespread misinformation. Even with the potentially good information out there, there is a general lack of credibility, especially where medical issues are concerned. Responses to certain medications, especially antibiotics, varies quite widely across the board. Perhaps I've just been unlucky, but I can't recall a fish that I've treated with antibiotics that's been able to make what I would call a full recovery. If you go to your fish medication aisle, every medication basically claims that it treats everything from parasites to bacteria to fungus--and that's just not true.
Medications also tend to come in packets of powder or tablets meant to treat 10 gallons or more. I start really sweating when I'm basically forced to cut lines of antibiotic powder like a coke addict--it's about the only way I have to dose the antibiotic, but it's still just an approximation of a dose that should really be much more exact since antibiotics are really serious stuff when you're dealing with a 2" fish. You run into a similar problem with tablets--there's no way of knowing how the active ingredients are dispersed across the tablet, so when you break it into a portion that is approximately the size you need, you're still not really sure if the dosage is correct or not. How hard would it be to put a dinky plastic spoon or something in the medication box that helps you dose smaller tanks? :/
The biggest drawback by far is just the fact that bettas are little heartbreakers. They've been so over-bred in such an irresponsible manner that even when you take excellent care of your fish, sometimes it just isn't meant to be. Sometimes all you get is a few months. If you're diligent and a bit lucky, they may choose to stay with you for 3-7 years. The luckiest number I've gotten was a 4. The worst part is that every time you lose one there is always guilt--moreso than with a dog or a cat, because the fish is completely at your mercy.
Another inconvenience is the fact that there aren't many readily available products for humane euthanasia of fish. The use of clove oil is generally accepted, but it hasn't been officially approved as humane by the American Veterinary Medical Association. Finquel is an anesthetic can be used for these purposes, but it's something you can't just find in your local pet store, and it's pretty expensive--another problem with it is that once the fish is anesthetized with it, it's hard to tell when the fish has truly expired past the point of reviving. All in all, fish euthanasia is a very stressful thing that puts a lot of pressure on the owner.