I'm, very, very late responding to this, so apologies for that.

I agree that getting into a top law or medical school is exceptionally difficult. Here's the admissions page for ucsf

http://meded.ucsf.edu/admissions/successful-applicant-profil...

Interestingly, they don't give admissions rates, but we can see that only 6% even get an interview. The numbers themselves are high, too. Looks like about 95%ile MCAT scores, and a high (nearly 3.8) GPA overall and in the sciences.

Law has similar numbers, though LSAT scores tend to be a bit higher - above 98%ile. My guess is that this is because law doesn't have the "weeder" courses in pre-med, so you do have a lot of high GPAs in history or other relatively easy majors.

Engineering is a very, very difficult comparison to make, because it truly is not the same thing. Licensure is unusual, largely limited to a couple of specialties, and happens (with exceptions) at the undergrad level anyway. Legally speaking, you don't need an MS or PhD for anything, and you rarely need a BS either. This of course is a big factor when thinking about admissions and attrition rates.

Still, there is a large PR effort in the US to convince the public and young people that there is a shortage of US Citizens going into "STEM" graduate programs. I've posted a link to a RAND study that concludes that this aversion is rational and market driven when you consider the pay and career prospects relative to the "professions" (medicine and law, as well as dentistry, MBA programs, even nursing and pharmacy... in SF, dental hygienists earn, on average, about 98% of a software developer's median salary).

Here's a link the RAND study

http://www.rand.org/pubs/issue_papers/IP241.html

It's very difficult to compare with graduate engineering programs, since they tend to be specialized at the degree level (rather than through residency in medicine or career choices later with law). But looking at entering class profiles, top engineering programs appear to be very selective. Not as selective in terms of admissions rates as medicine or law, but I think this is more a function of very heavy course requirements for admission (you can major in anything for law, and you can do pre-med in 2 years, whereas to apply to an MS or PhD program in engineering, you tend to need essentially 4 years of exceptionally difficult specialized coursework).

So admissions aren't really notably easier for graduate work in engineering, undergrad prep is very hard... and yet, attrition rates are brutal. Overall, engineering is the best of the bunch where PhD attrition rates are concerned, at about 35%. In hard sciences, these typically go up to about 50%. This is for a cohort that has gotten top grades in majors like physics and scored at least above the 90%ile on standardized tests, usually quite a bit higher.

In short - I'm willing to agree that getting into law school is tough, but not any tougher than getting in to a top grad school in engineering (probably much easier, when you consider the coursework you need to take for engineering), and getting through law school, based on attrition rates, appears to be far, far easier. Even med school appears far easier from an attrition rate point of view. They're hard working, sure, but so are grad students in STEM. I just don't think hard work can explain a difference in attrition rates between 50-100 times higher.

Of course, like I said, you don't need a PhD or an MS to do anything in engineering, so maybe they're not really useful as a point of analysis here. The reason I bring it up is that there is still a strong PR push to get more young US citizens (or these days, women) into STEM graduate programs, and yet the numbers are horrendous for that path. Difficult coursework, sky high attrition, and - at the elite level, since we're talking about "best and brightest" - mediocre outcomes compared to medicine and, at the elite level, perhaps law as well (and many other fields).