Why are J-dramas really short?

Usually J-dramas don't stretch out their contents unnecessarily like you see in K-dramas.
Also I think, it has something do with the season chart they follow. From my point of view they divide the year in 4 seasons. Winter ,Spring, Summer & Fall. Each consisting 3 months and each month more or less 4 weeks. A episode every week, so that's around 10-13 episodes per season.
Most western TV shows also follow a episode each week but if the ywant to extend the season to like what you say 20+ episodes then they definitely take a mid season break in between(like 10 episodes of first season in winter then after a few months gap rest 10 episodes).

But at the end of the day, if the series can manage to contain everything in 10-12 episodes then I don't see any problem. In fact, it's much better. Who wants to watch fillers after all?

not all of them are, but mostly.

They usually only have like 9-10 eps, but the eps can be 30-50 or even an hour long which I like. 

I do sometimes wish there were more though.

As a watcher of both K-dramas and J-dramas, I wouldn't say J-dramas are short, so much as they would be better if they had more episodes. Most are 10 or less episodes, so they have to start wrapping things up around episode 6... it would be better if they matched anime and had more like 11 to 13.

For K-dramas, they seem to average around 16 episodes, which is often too long as you frequently get the feeling they are doing filler in episodes, because they really only have story for about 12 episodes.

I've watched a couple of asadoras and I really wish they would re-package them into like 30 to 50 episodes of 45 min to 1 hr. They tend to be high quality, but you get the feeling 25% of each episode is theme song and recap.

A better question is, why are K-dramas so long?  Most of the K-dramas that I've seen dragged on for too long, but J-dramas are usually just the right length.

Like other people pointed out, there are some longer ones, but 10-12 is the most common length.