The very fact that you need to ask this question, in a way, provides its own answer.
One of the primary functions of academia is to teach the skills of research. There are two aspects to this, both critical; first, being able to find what work has been done by others and, second, to do new work yourself. Without the ability to effectively do the former you risk wasting time repeating pre-existing work when it comes to the latter.
Now, for non-academics, Wikipedia has rapidly become a catch-all, sole source, and generally fantastic one-stop shop for information. While this is well and good for casual use, it nevertheless provides an enormous disincentive to acquiring and practicing those critical skills of research that you will need if you intend to continue to pursue a career in academia.
My feeling is that most professors are, even if subconsciously, objecting to Wikipedia for this reason above all others. It feels wrong to them because it is a shortcut -- a cheat that puts a stop to a student's research effort before it even begins. In their own careers they have a deep appreciation for the need of strong research skills and, likewise, an appreciation for the need to teach those skills to students.
If Wikipedia ceased to exist at this very moment, ask yourself the question - "Where would I find information, and how would I go about doing it?"
In the world of academic research, this is the situation you find yourself in - beyond a certain level, Wikipedia will not have the answers you are looking for and you will need to have developed more advanced research skills to find them.
By artificially outlawing Wikipedia, professors are attempting to simulate what the real academic world is like - one where the answers are not already known and easily accessed; one where you, the researcher, are tasked with needing to know how to effectively dig deeper to answer questions for yourself.
The critical thing to realize is that higher education is not like primary school anymore. The error you are making is in thinking that an assignment about topic-X is chiefly intended to populate your brain with information about topic-X and that the most effective means of getting information about topic-X into your brain is the best solution to the problem.
This is wrong.
Topic-X is largely irrelevant. The real task is to teach you the skills you require to find information about any topic. Topic-X is simply a convenient and concrete sample of a topic on which to learn and practice those skills. That the information on Topic-X is readily available on Wikipedia is merely a reflection of the fact that, as a junior academic and undergrad, you simply (at the moment) lack the technical education necessary to be given a more advanced "practice" topic to research - one that would not be so readily found on Wikipedia.
Nevertheless, the professor's objection to Wikipedia is for a very clear reason - it is entirely counterproductive to their primary (and probably unstated) objective of getting you to exercise and develop real research skills.
Consider the broader context.
From a slightly different perspective, in a lot of ways Wikipedia has really raised the bar. If you are a university student and you are working towards a degree in a subject then it bears considering what that means. If any joe public can look something up on Wikipedia with the most minimal amount of effort then what does that mean for you?
Surely an academic degree needs to be something much more than a certificate proving that you know how to type "X" into a wikipedia search box. A child of 6 can do that these days - if you're looking to gain a serious academic qualification then you really need to be going above and beyond what has become this most basic level of ability to research information.
