I was in the same situation as you when I took precalc (I will be starting my freshman year in college in a month) except we were never even exposed to counting methods. The only time counting methods were taught were in my geometry class and for no particular reason except that the administration felt that students should learn the basics.
I think one of the reasons counting and probability is an area of struggle, at least here in America, is that our typical math curriculum is nowhere near ready for such topics to be included. I went to a very good high school and even then there had to be compromise and trading to find the right teacher with the right knowledge(who didn't teach geometry) to teach us counting. I think you'll find many less K-12 teachers who have a firm head for combinatorics than for algebra. But even that there are many less than qualified teachers in the latter subject.
Granted that the ultimate goal of a K-12 math education is to prepare students for calculus, an early exposure to discrete math may keep more students interested in mathematics. But this doesn't look like it will happen anytime soon.
Anyways, as a consequence, most people are exposed to and familiar with continuous mathematics. I think in some cases this lends to the person having a difficulty (at least initially) with discrete math. As for myself, I have definitely improved in number theory (which I knew just as much about in precalc as I did about counting, practically nothing) but I will admit I have been avoiding counting/probability a bit. I guess I want to know if having an aptitude for one area of discrete math will lead to improvements in another.