Figures in a results/discussion page
I believe that I strongly disagree with your professor.  I can barely imagine writing a results section that is not filled with figures, there to compactly present critical, graphically summarized information about the results. In fact, one of my key early triage steps in reviewing a paper is to flip to the results section and see if there are any figures: if there are no figures, then it is very likely to have insubstantial results. Now, this isn't always the case---some papers have only theorems as results (though figures often help explain such theorems), and some have only a few key numbers in a table (though is a table a figure?)---usually, however, no figures means not much in the way of results to present.

I think that it is also a mistake to divide figures from prose and try to decide which is the "star" of a results section.  In a well-written paper, they serve complementary purposes: 


Figures are better for presenting numerical relationships, non-linear structures, and high-density data.
Prose is better for presentation of isolated or non-visual elements, directing the reader's attention to the most important aspects of the results, and explaining the significance and relationship of the results to one another and to the larger scientific investigation.


These two can and almost always must play together harmoniously in order to effectively present a scientific work.

For a lovely introduction to what makes an effective figure and a good source of inspiration for your own work, I would suggest reading Tufte's "Visual Display of Quantitative Information," a classic work on data visualization.