(I want to preface this by saying that I'm talking about people storing their savings in Bitcoin. If you don't care about what happens to your money, then it doesn't matter whether you trust Coinbase.)
The most convincing argument, I think, is that you're putting your faith in an entity that's not FDIC insured to hold onto your entire future and keep it safe. Your savings is your future. If you lose it, you lose your future. You'll have to exchange months or years of your life to get it back, as I now have to. There are many reasons that businesses fail, and it's important to never forget that Coinbase is a startup, and the fate of startups always hang in the balance.
There's no reason not to trust an entity that's ensured by the government (banks) with your savings. They won't vanish.
The only reason right now to trust Coinbase with a lot of money is if you're hoping the price will rise, as far as I can tell, because there's no other realistic application of Bitcoin right now unless you want to send some money to a friend, in which case you can just buy it as-needed. So it's essentially long-term gambling. Now, there's nothing wrong with that. I knew when I did it that there was a chance things could turn out horribly awry (though I don't think I fully appreciated how "down" the downside could be for me). But if you're going to do it, at least be smart about it: The coolest thing about Bitcoin is that you don't have to trust anybody but yourself to keep your coins safe. There are secure cold storage wallet solutions. Find one, use it. I've heard good things about Armory, for example.
Look up some of the stories of people literally becoming homeless due to losing their coins when they were stolen from Silk Road 2. People aren't rational. They don't store "just what they can afford to lose and no more" in a webwallet, apparently.
You could counter that by saying "Oh, those are just drug addicts. Normal people aren't that dumb." To that, I can point at the example of the Mt. Gox collapse. There you have a case of people going from millionaire status to "looks like I'll have to find a job and keep it for a long time" status in the blink of an eye. One of the bigger losses was 4,700 BTC: http://www.reddit.com/r/Bitcoin/comments/1yv26o/gox_horror_s...
And lastly, you can't have it both ways. Either Coinbase is trustworthy enough to keep your personal savings safe, or it's insane to trust them with any amount of money that you care about not-vanishing.
(I want to preface this by saying that I'm talking about people storing their savings in Bitcoin. If you don't care about what happens to your money, then it doesn't matter whether you trust Coinbase.)
The most convincing argument, I think, is that you're putting your faith in an entity that's not FDIC insured to hold onto your entire future and keep it safe. Your savings is your future. If you lose it, you lose your future. You'll have to exchange months or years of your life to get it back, as I now have to. There are many reasons that businesses fail, and it's important to never forget that Coinbase is a startup, and the fate of startups always hang in the balance.
There's no reason not to trust an entity that's ensured by the government (banks) with your savings. They won't vanish.
The only reason right now to trust Coinbase with a lot of money is if you're hoping the price will rise, as far as I can tell, because there's no other realistic application of Bitcoin right now unless you want to send some money to a friend, in which case you can just buy it as-needed. So it's essentially long-term gambling. Now, there's nothing wrong with that. I knew when I did it that there was a chance things could turn out horribly awry (though I don't think I fully appreciated how "down" the downside could be for me). But if you're going to do it, at least be smart about it: The coolest thing about Bitcoin is that you don't have to trust anybody but yourself to keep your coins safe. There are secure cold storage wallet solutions. Find one, use it. I've heard good things about Armory, for example.