Why is MATLAB used so much in industry when there's other software that can do a better job?
Matlab is largely equal to Mathematical is largely equal to Maple. Just because you are more familiar with one does not make it "better".

The reason Matlab/Mathematica/Maple are popular are because they are much, much easier to get started in then C++/most programming languages. They come ready-to-go with everything you need to draw graphs, do differential calculus, whatever.
Furthermore, there is a help system. 

All this makes them dramatically more appealing to people who are not computer science majors (e.g. mathematicians, biologists, physicists, etc...). 

As for your professor taking two hours to find a transfer function.... What? The first google search result for "Matlab transfer function" is the mathworks documentation page on the matlab transfer function.



As an aside, python is making significant inroads on the mathematical computing world, primarily because of it's philosophy of batteries included. While the default plain python install isn't particularly targeted and scientific computing, there are specific distros that provide a environment similar to matlab straight from a single install.

Python also has the benefit of being much more powerful and flexible the purpose-specific languages like Matlab/Mathematica/Maple. Python started out as a general language, matlab started out as being a language for math students, and bolted on general purpose tools later on.