I think what this is illustrating is many people would not see this as a contradiction.
Taking a step back, there are quite a few people who believe college is really too early to try to be teaching people how to be really good at a specific profession. A lot of that practical education actually happens on the job, of course–interns in medicine, junior associates in law, various similar entry positions in different business fields, and so on. And then even the educational step before that often comes after college–the MD or JD obviously, and then while MBAs are not always required, they are often helpful, and those typically come after both college AND work experience. For that matter, med schools and law schools are also increasingly interested in people having some sort of prior practical experience.
OK, so you are entering college with like none of that, and a lot of people very much believe you are not in fact ready at that point to start a specifically professional education. Instead, they think you should continue getting a good general education. Even med schools do not require specific degrees, just a broad education that includes the various subjects considered important for future health professionals.
And so it is absolutely no surprise that independent LACs like Amherst are considered by many to be excellent colleges for pre-professionals. Because they are very much still PRE professionals, and Amherst and such are great at providing the general educations such people think you should be getting in college.
Indeed, this is really no different from the LACs that are not independent but are instead embedded in prominent private universities. Colleges like Harvard, Yale, Princeton, and so on ALSO do not offer professional degrees to their undergraduates. Harvard and Yale, of course, have some extremely important professional schools (not Princeton), but they do not make those schools available to their undergraduates because they are similarly in the tradition of thinking it is too early for that when you are still just in college.
OK, so I don’t think a lot of people question whether Harvard, Yale, Princeton, and so on are good places to go for college if you are interested in a professional career. And that is really no different from why LACs like Amherst are also very good for the same purposes.