Why is it so bad to up your run mileage too quickly?

If you already had a 5K base, going up to a 10K quickly isn't a problem.  It's really not that far of a distance.  However, when you are going beyond a 10K, you really should mileage build about 15% per week.  The purpose is injury prevention.  You need to get your muscles to understand what's going on.  It also strengthens ligaments, tendends and bones!  I've known several people to NOT mileage build and end up with stress fractures in their tibia and fibia.

In short - mileage build if you plan on increasing past a 10K.  You'll only help yourself.

Injury risk is the main concern.

The 10% per week guideline that is often mentioned is nothing more than that. Some can handle more, some less. Also, intensity matters, such that high intensity workouts are more stressing on the body than easy miles. 

How often are you running currently? Do you have the room to add more days per week? And are you going to be in a position to do the workouts as all running (as slow as needed), rather than run/walk?

Yes, the normal result in upping mileage too fast is injury.  It won't happen in 2 runs, or even two weeks of runs.  It usually happens right when you're feeling terrific.  So good that you pretty much ignore that little pain in your hip, or foot, or shin, etc.  then it gets worse.

But- go for it.  in order to improve, you need to put some new stresses on your body.  Just listen to what your body has to say in return.  You should finish each and every one of your runs with the feeling that you could do more (except race day- then, leave it all on the course).

The last 2 post are spot on in my opinion!

I didn't have the types of injuries mentioned in those posts but I had had an ACL reconstruction and the meniscus tears that go with it and a quick mileage increase WITHOUT the 4th week recovery (as mentioned above) cause me to re-injure one of the meniscus and have another surgery.

Stick to the above 2 posts and you'll be fine.

Bingo.  Did this in April.  Still paying the price six months later.  I decided to bump my base run mileage by about 15-20%, and upped my pace from 9-9:15 min/mile to 8:15-8:30 at the same time.  I knew that I was risking an injury, but wrongly figured that I would feel it coming on and that it would just be my typical achilles strain which I could rest for a couple of weeks.  Anyway, I had planned to do this for a couple weeks and then back off.  But by the end of two weeks, I had caused myself a new problem, which I still haven't shaken, even with some long layoffs.  Anyway, not looking for pity, just reinforcing your point.  When it comes to intensity and volume, up one, but back off on the other.  Both at the same time isn't a good idea.

Just to throw my own experience on this.  I was running around 20-25 miles a week through the summer and decided.  Hey, I'm going to run a lot more to get faster.  I ran 12 miles one day and then ran another 12 miles the next day.  10 miles into the second day my IT band started hurting really bad and I had severe knee pain on the outside of my left knee.
I was down for the count for a couple weeks and it almost kept me from doing my first Oly Tri.

Fortunately I let it heal and I'm fine now, but I learned the hard way that I need to gradually increase my mileage.   

This is exactly what happened to me.  I tried ramping up my milage too fast getting ready for a marathon and it was in the middle of a tempo run where I was flying effortlessly and feeling AMAZING that my IT Band finally went so bad I could run again at ALL for months.  I'm STILL not where I was, run-fitnees wise.

So in the words of Treebeard, "Don't be hasty."

I have been running about 3 times/week, which was only about 9 mpw.  I'm looking to up that to about 15 mpw or so.  The workout I did yesterday (treadmill) looked about like this...

10 minutes: walking warm-up

2 minutes at 5.5 mph

2 minutes walking at 4 mph

1 minute at 7 mph

2 minutes walking at 4 mph

1.5 minutes at 6.2 mph

2 minutes walking at 4 mph

Rinse and repeat for an hour

Finally, 10 minute cool down walking

So, I'd like to do 4-5 miles about 4 times/week.  I just feel like I really need to focus on running for the winter because I'm painfully slow and just don't have enough endurance.  I have a hard time running for a long stretch without stopping to walk, and I want to fix that.  I've only run a straight mile ONE time in my life, and that was about a month ago.  I really want to be able to run a few miles straight without walking.  I was the slowest one in my tri training course this fall, and it drove me nuts.  I just don't want to be the slowest person in the class in the spring.  Is that crazy?

I agree 7 mph is way to fast for 9 miles per week.  If you want to do more you can run your 3, 3, 3, and walk 1, week 1, then 3,4,3, walk 2, then 3,4,3,2 walk 2,  then 3,4,4,3,walk3, 3,5,3,4,2... etc.  Once you get to 25-30 mpw for say 3 months you can start focusing on adding in temp runs and mile repeats.

Right, go for 5 mph or so.  Just enough to shuffle your feet so that it's not a walk.  You need to be running continuously a lot more before you try to go faster.

It just isn't very fun to shuffle along, LOL.  There's something about bursting out with some speed that makes me feel like I'm not a complete slacker.  I'll try the shuffling, though, and see how it goes.

So, I need to actually get to where I can keep up a slow run pace before I do the speed stuff, then?  I was under the impression that "interval" training (I think that's what I was doing?) can help build my endurance because it's teaching my lungs to recover from more effort, thus making that shuffling pace more do-able.  You wouldn't think that running would be so confusing!

Follow a plan don't wing it.

Running 9 miles a week isn't a lot you need to be careful.

Yes, just start with the shuffle, if that's what you're able to keep running continuously. Keep doing it for a while and you'll find that it will start to become less shuffle-like.

Eventually yes intervals can help you build speed but at your mileage level simply running regularly will help you increase speed.  Endurance build comes from the run more, mostly easy part.