I've noticed this too and tend to agree with your observation, but I don't think this is necessarily because certain people don't get or are not naturally talented in a specific subarea of mathematics.
My math professors told me that math majors tend to fall in love with the second upper-division math course that they take, because in the first one, you're still struggling with the details of moving from mostly computational to proof-based problems. Usually this first course is either real analysis or abstract algebra, and since all analysis and algebra classes tend to build on the fundamentals of these courses, this may show up in the subsequent classes that you take within these fields.
I can understand the PhD part: the programming involves a different mindset than bio and chem: "It's more of a craft, than an art" -- a neurobio PhD. To paraphrase, it is more dependent on wisdom than cleverness.
The math tidbit is interesting though. What other examples have you seen of good mathematicians being lopsidedly talented in one area? What kinds of areas were these? I can somehow see real analysis involving a different ability than that of discrete math.
Most mathematicians are "lopsidedly talented" in one area, typically that of their Ph.D. You rarely see modern mathematicians who are able to understand--much less make significant contributions to--current research in many different fields.
Yes. When I was getting a math degree, people who were really good in one area, like analysis, often struggled in another area, like abstract algebra.
Likewise, when I lived in Boston I worked with PhDs in microbiology and biochemistry who had a hard time with computer programming.