why is belt drive better than direct drive?

Belt drive are generally quieter. As Celtic said, results may vary. I have a vintage Dual United Audio direct drive from the early 70s and it outperforms my Dual 505-2 belt drive.

Belt drives typically offer better isolation of motor vibration. Whereas a direct drive unit has the motor "directly coupled" to the platter / record / arm / cartridge interface, the only thing linking the motor to those things is the belt. Depending on how the motor is mounted and the shape / size / material used in the belt, most of that noise can be minimized or at least drastically reduced. While there may be some technical advantages to direct drive, most of them are overcome by using "fresh" belts on a belt drive. While old belts tend to stretch and increase speed irregularities via slippage, ANY motor variations or vibration in a direct drive unit is instantly transmitted to the platter with NO damping whatsoever in a direct drive unit. Like anything else, there are pro's and con's to each method. As a case in point, ask a "DJ" or "scratch mixer" which type of table they prefer. It will most certainly be the opposite of what is considered to be the audiphile "norm". Sean
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The direct drive turntables do not have a belt wearing and pick up faster.
Sonically there are disadvantages only.

Sean has said it all. I have nothing to add to that, except that getting new belts can sometimes be quite a bit of a drag. Incidentally, beltdriven CD players, if TAS is right, seem to have the same sonic advantages over direct coupled ones, as turntables for vinyl.

As Sean said above, any variation of a DD motor is tranmitted to the platter. That's the big rub: speed changes. Most DD motors are constantly increasing and slowing their speed to adhere to the desired speed setting. These speed changes may be minor as a percantage increase or decrease of overall speed, however, even a miniscule change will affect pitch.

And perfect pitch is what it's all about, eh?