Okay, I'll hit the failure in health sciences first.
I was near graduation, and I was sitting in the hallway with a bunch of my fellow students waiting for a class to open. I was taking "biological psychology" (I think the course had a different heading but that was the name of the text, and what everyone called it.) It was the study of human and animal nervous systems, sense organs, and cognitive processes, all the way from the synapse up to the whole organism. Wow! It was really fascinating! It was basically Which-part-of-the-brain-does-what and what-happens-when-something-goes-wrong. A lot of the functions are inferred from what is missing when a particular part of the brain is destroyed. A guy sitting next to me in the hall, also near graduation, was looking at a map of dermatomes and neural pathways, and talking to his classmate about neurotransmitters too. I asked him if he was taking another section of biological psychology, because I thought that there was only one. He answered that he was in anatomy and physiology. He seemed frustrated... He was in pre-med; he was going to be a doctor. He asked me why I was enrolled in my class, and I said that it was a matter of interest, actually I'm an art major. I asked him if he liked the science behind it. "No, not particularly." he said. I asked,"Well then you want to help people?" "No, not really."
"So, if you don't like people, and you're not into the science and research part of it, why are you going into this field?"
His reply made my heart sink (and I quote): "The extra eighty thousand a year I'm going to make is going to make me like it."
I felt that I was looking at a future unhappy, disdainful, error-prone doctor.
The medical field is lucrative enough that you'll have a bunch of people who are only in it for the money, and a lot of those are going to smash up against the requirements of the classes.
Concerning the sciences in general, one problem is that there are many people who will have trouble visualizing a lot of the concepts in their minds' eye.
My main objection to trigonometry and pre-cal was that it started off very jargon-heavy. There are a lot concepts that the teachers and T.A.s consider to be below the starting point. Most people seem to only want to memorize the formulas, and as long as they can plug in the numbers and it works, a lot of them don't really care How it works. I'd say, "wait a second, then what is the cosecant?" And they'd say, "Yeah, it's the reciprocal of the sine." by way of complete explanation, and smile, not realizing that I didn't get a visual understanding of what was going on. It wasn't until I pursued simple computer graphics that the unit circle suddenly snapped into focus. "Oh! It's just the Pythagorean theorem, It's just that the hypotenuse always equals one, so that means that an x or y coordinate can never be bigger than 1, and once you know one side, and that the hypotenuse is 1, then the other side comes easily. I was too literal and wanted to give answers like 0.8660254037 like it was an x-coordinate, or 1.5707963267.
I was uncomfortable giving symbols as answers to math problems.
Astronomy was a breeze because I already had so much interest and the new information plugged right into the old slots I already made. If one is really eager about the subject, one will read ahead, and the actual course material will seem like review, but if one is not interested and has trouble making any brain-space for it, it will be rough slogging. The biologies were easy enough for me that sometimes if I knew that I was going to be taking classes in my weakest areas (e.g. Poly-sci, Foreign Language) I would take another biology course to prop up my GPA.
Another problem is that the math helps the visualization and vice-versa.
Again, I guess I'm too literal, my thinking is too concrete, for me math has to describe something, acceleration, great, volume of a sphere, cool, compound interest, alright, vector addition, now we're talking! To me stats and something like standard deviation makes more sense, and is easier for me to comprehend than some concepts in plain old algebra. You have to admit that a lot of algebra is just number juggling without describing any phenomenon.
A lot of the concepts in physics are counter-intuitive, I believe that's because much of what is measured by our instrumentation goes against what our senses are telling us.
Take the inverse square law for example:
If a light bulb is shining through a square hole in the wall that is 10cm x 10cm (say one meter away from the bulb), a certain amount of light is going to go through that hole. If you have the light shine on a wall another meter behind the hole, the same amount of light has to cover a 20cm by 20 cm patch, it's spread out over four times the area, yet it only looks somewhat less than half as bright, at three times the distance, only one ninth the flux, which is surprising because it looks kind of like it's a little less than a third the amount of light. It turns out that the human eye is a logarithmic detector. (That's why the first 60 watt bulb you turn on in a room adds a lot of light, and the second 60 watt bulb you turn on only makes it a little brighter, instead of TWICE as bright.) Our eyes evolved this way to cope with the extremes of energy in our environment, and to pass on relevant survival information about the organism's habitat, however it also edits down information before it ever gets to our brains, (and so it goes for most of the rest of our senses) so we think that what we see is what we get. It's hard to ever get past that, and I think a lot of people never do.