So instead of spending Bitcoins, I should just save them and spend dollars, because if I have a whole Bitcoin token when people are trading in millionths of a token, I am a millionaire. Sounds like a currency that has a pretty dim future...

No because you'll eventually have something come up that makes you want to spend those bitcoins, even though you know they'll be worth more in the future. and when you do so, you'll be getting a significant effective discount on your purchase. For example, if you bought bitcoins now at $12, sat on them like a good little hoarder, knowing they'll be worth $1000 in 5 years and all of the sudden you need a new car and the bitcoins are only worth $24, you're getting a 50% discount on your car purchase by spending those bitcoins.

This argument gets made frequently. Here is a response from the bitcoin community. https://en.bitcoin.it/wiki/Deflationary_spiral