Is butter required to caramelize onions?

Onion can be caramelized without butter. Or any other type of oil. However, unless you are actively avoiding using fat, there really is no reason not to.

The main benefit of using oil when caramelizing onion is the fact that oil can reach a higher temperature than water. To caramelize onion you need to reach about 230F. Water boils at 212F and will not go higher than that. So to caramelize without oil, you would first need to draw out the water and "dehydrate" the onion a bit before they reach temperatures that can caramelize the onion. Note: Never put water into the pan if you wish to caramelize onion.

The reason you very commonly see butter used is because it can reach temperatures above 230F and it's flavor profile works really well with the savory sweet flavor of caramelized onions.

As others have said here, butter isn't required. The browning and good flavour come from the maillard reaction:

https://en.wikipedia.org/wiki/Maillard_reaction

You can use oil instead of butter, though the flavour will probably be a little different. You can also add a little baking soda, as the increased pH will increase the maillard reaction, which gives more great flavour faster. This article has pictures comparing caramelized onions with butter vs oil, and with vs without baking soda:

http://www.seriouseats.com/2015/01/how-to-make-the-best-french-onion-soup-caramelization.html

You can also use a pressure cooker, in which case you can achieve a temperature high enough that the maillard reaction occurs, even in a wet atmosphere. At normal atmospheric pressure, you'll never get past 100 degrees when there's water, but under pressure the temperature is higher. That's one of the reasons pressure cookers are a great tool, you can use them to pack more maillard goodness into soups and sauces, for example.

Butter is not necessary. In fact, you can caramelize without any fat. The browning of the sugars in the product is what creates caramelization. To caramelize without fat, chop or slice onion, place in pan with a little salt. Cover and cook at medium for about 5 minutes. Uncover and cook any water out. Stir often. Deglaze the pan with a bit of water. Cook and deglaze until you reached your desired effect.

No, you don't need butter to caramelize onions because they are very very sweet, and the sugar inside of them is what become brown as you caramelize your onions.

They do however get pretty sticky since you are basically creating caramel, so if you're not using butter, you should use some oil, or have a very nonstick pan, or you will struggle trying to scrape the brown bits at the bottom of your pan, and they might burn.

They brown and become flavorful for two reasons, not one: Two different browning reactions are at play in the process: caramelization, in which sugars break down into hundreds of new molecules ... and the Maillard reaction, in which proteins and sugars transform into an insane number of new flavor and aroma molecules.

https://www.seriouseats.com/2019/06/how-to-caramelize-onions-classic.html

Serious Eats is a very good site for the best methods bc they focus on the science behind the techniques and also are invested in creating the tastiest, most appealing food they can. (Its director, J. Kenji Lopez-Alt, is a James Beard winner.)

With respect to an earlier poster, you not only can put some water in the pan, you'll have to (as the fond increases and needs to be scraped up).

Also, I'm pretty sure I learned years ago on America's Test Kitchen (another science-based resource) that certain bitter compounds in the onions will break down in butter but not in oil, but I can't substantiate that claim. (I've tried both and find that the onions retain some bitterness when cooked in oil. I share this info unhappily bc it's at odds with my concerns about animal welfare.)