That "Harvard Professor" is David Malan who has been running "CS50: Introduction to Computer Science" course at Harvard (https://pll.harvard.edu/course/cs50-introduction-computer-sc...) for a while now. So presumably he has good experience on the pedagogy needed in the teaching of CS and what they believe is necessary in the curriculum.
As a person who has been doing C/C++ for over three decades now, i can confirm his points and add the following for an even more compelling story;
1) C is the interoperation lingua-franca of the software world due its defacto "standardized" ABI.
2) C allows you to program all systems from Desktop/Server to all Embedded MCUs (simple or complex). This is huge since there is practically no limitation on what you can attempt.
3) C allows you to work at all levels of software viz. Applications, OS/Compilers/System Software, Bare-Metal. This too is huge since there is nothing really hidden from you thus allowing you to move up and down the software stack based on your interests/needs.
4) Finally, there is a ton of C code out there which people still need to understand, maintain and extend as needed. Many of them are critical infrastructure viz. OS Kernels, Databases, Web servers, Automotive/Aviation systems etc.