How do you actually block someone?

Will do, thank you!

I've just checked multiple ways of accessing a profile, and used several profiles as well, and the block option is open and available everywhere I've checked. Either he has already blocked you (which doesn't make sense) or you need the help of either customer service or tech support. Just email one of them and briefly explain the problem and what you're trying to do (and what you can't do) and perhaps they will do it for you.

I don’t see any block options. There are icons that are greyed out and unclickable. I would post a screenshot but this form doesn’t have the option to attach an image.

You need to go to his/their profile and find the block button.

We don't use the im feature so we don't know if you can block from there.

On the profile page, below the photo but above the bulk of the text are two rows of icons. The far right one on the first row is "Block."

I’d like to block a user who initially initiated contact via chat and had become argumentative after I honestly explained we were not looking for the same things and that I was backing away.
The only option I have found to block a user is a link labeled BLOCK on the page of a Message. I cannot find any such links from the chat or profile pages.