HTML is not a programming language. While some may point out that HTML is a "markup language", this doesn't clarify how that is different from a programming language. I'd like to provide a simple reasoning that is easy to understand by the layperson. (This isn't meant to be a thorough argument, but rather a brief explanation that goes just a bit more in detail than "HTML isn't a programming language but instead a markup language.")
Here is a point I'd like to make: HTML is no more a programming language than Microsoft Word is. With Word (or any other word processor software), you can write out text and format it with different fonts, sizes, and colors. Images and tables and bullet points can be added as well. This is all done through the word processor's graphical user interface.
An HTML file is similar, except it does not have a GUI. Instead, it is entirely written out in plaintext, so all the formatting instructions must be typed out as HTML tags (for example, <b> or <center>.) This "language" of tags is how we can format the appearance of a webpage.
Programming languages, on the other hand, can process data and make decisions. You can store data such as text strings and integers, and then manipulate these values to perform calculations. For example, doing some math or sorting text alphabetically are kinds of data processing that you cannot do in HTML.
Programming languages can also make decisions about what instructions they should execute. Depending on if a certain condition is true or false, a set of instructions may be executed or skipped by a program. Here is a Python example of such code:
if password == 'rosebud': print('Access granted.') else: print('Access denied.')
Programming languages also have ways of executing instructions over and over again in loops. Loops, if-else statements, and other such instructions are called flow control statements. All programming languages have these flow control statements, but HTML (and Microsoft Word) do not.
Because HTML lacks these features, it cannot be called a programming language. One does not "program in HTML" nor could one "write HTML code". You should never list HTML on your resume under "programming languages".
The difference is not just a snobbish opinion of elitist software developers. While this post is by no means the definitive and complete reasoning of what a "programming language" is, it is good to know the general difference between a programming language and HTML.