Part of the reason I think a lot of hard scientists look down on biology is that introductory biology is so often poorly taught in a particular way. Intro physics is almost entirely problem-solving, and intro chemistry is similar, with maybe a bit more memorization (Quick! How many valence electrons does aluminum have?). But biology frequently ends up being taught as a large heap of random terms and facts, almost entirely without any unifying themes or methods of thought -- just a disconnected jumble.
I've dubbed this "trivia-heap syndrome".
Any biologist (or, hell, anyone who's gotten past the required intro course) can tell you that biology is not about memorizing terms and facts, any more than physics is about blocks sliding down inclined planes. But as Chad Orzel says in that post: "To some degree, this is inescapable-- those repeated exercises are used to establish a pattern of thought that is a necessary prerequisite for moving on to more interesting material." A similar thing could be said of biology: to some degree, it's necessary to memorize a lot of terms and random facts and unconnected processes and so on, before you can get to the interesting work of studying how they interact and how they can be manipulated.
But this is actually true of every field, not just biology (or other fields prone to trivia-heap syndrome); it's just not as apparent. Consider intro mechanics again: all about things falling, hitting each other, rotating, etc etc. In order to do interesting things, you first have to know what balls, rods, strings, pulleys, blocks, inclined planes, and gravity are. You also have to understand the basic types of things they can do: move, rotate, accelerate, come into contact, break, exert forces on each other. Of course these are trivial things to know, because we've all been exposed to simple objects and their motions since we were born -- and this is why intro mechanics courses don't begin with a couple weeks of definitions and memorization. The only difference between that and biology is that we're not exposed from birth to genes and proteins and cells and their interactions. The world teaches us the trivia-heap for physics, but we have to be taught about biology's trivia-heap.
All right, so the trivia-heap is an unavoidable evil whenever you're starting in a new field. Fine. But never fear, there are still ways to get around trivia-heap syndrome. As soon as you know a very few things, you can start thinking about them in terms of experiments to be done and puzzles to be solved, instead of facts and descriptions. What would happen if this particular thing were mutated in this way? What effect would that have on the cell? How could you (the experimenter) tell that this was in fact the case? What if you got the opposite observation -- what might have gone wrong? Here's a simple system you're interested in; outline an experiment to find out whether this particular part of it works this way or that way. This is both interesting and a lot more like what actual biologists do; certainly much more so than the typical dreck of "Define a gene", "Outline how a gene gets translated to protein" that most high-schoolers get shoved down their throats. That's lazy teaching for you (or the creeping horror of bad standardized curricula for things like AP tests, which reduces to the same thing).
I learned a decent bit of biology just by reading random things. I can practically recite The Cartoon Guide to Genetics, by Gonick & Wheelis (that link is to the updated edition, not the old-school edition I read). I also took an introductory class at one of those academic summer camps. The net result was that I came into my high school biology class already knowing about half the stuff we would cover, which just made the trivia-heap syndrome that much more painful. A lot of my classmates struggled with memorizing things. Very few people did well on the "lab practical", in which we had to plan and carry out experiments to identify a mystery substance -- precisely because we spent so much time on trivia-heaping and so little time on problem solving / sensible experiment design. MIT's intro biology course (7.013), by contrast, is like a breath of fresh air. It's not entirely free of trivia-heap syndrome, but there's a gigantic emphasis on solving puzzles, considering what-ifs, proposing experiments, and interpreting results. (`Gigantic' emphasis relative to other intro biologies, of course.)
Granted, even MIT's intro biology problem-solving is simplistic, and occasionally feels like doing an inclined-plane problem in physics (especially when I know a decent bit about a particular system, and I can tell the problem vastly oversimplifies the situation, even if I don't know exactly how). But now we're back to Chad Orzel, inclined planes, and "establishing patterns of thought". There is a certain intuition of biological ways and means, of how cells/genes/proteins work in broad strokes, that is immensely valuable but hard to obtain. This intuition is something like a toolkit of abstractions over specific examples, but I'd venture to say it's not something that can be taught explicitly in the abstract, the way math can. The analogous thing in physics, again, is something the world teaches us from birth: unsupported objects fall, if you push something its speed changes; that sort of general idea about how things operate. I've developed my biological intuition somewhat, through reading and studying (and sometimes working directly with) boatloads of examples, and I think that's just about the only way it can be developed. But it's something every experimenter (or bioengineer!) needs in spades, and it's something the general public could also really use.
So, to sum up: the trivia-heap is sometimes a necessary evil, but trivia-heap syndrome is eminently avoidable. Emphasize puzzle-solving and experiments, instead of facts and definitions, and it'll do everyone a heap of good.