If I’m in a fight, I’m fighting. If I’m on a walk, I’m walking. On a hike? Hiking. If I’m at a party, I’m partying. If there’s rain in the air, it’s raining. If I’m applying butter to my toast, I’m buttering my toast. If I’m on a boat, I’m boating. If I’m in the middle of a fall, I’m falling.

Everything before fall was a verb. If you're in a pool, you aren't pooling. If you're in a car you aren't caring. If you're in spring you aren't springing. (We do have words for summering and wintering, but they're actions you take, not just being in the season.)

Is it hard to understand that someone is referring to the act of entering Fall (or being in the middle of Fall) when they call it “falling?”

I get the joke. I was trying to make another joke by being pedantic, but now you're doing this. That is not how the English language works. You do not say your doing an action when you enter a season. You are entering Fall, but you aren't Falling. You are not doing something.

First, you don’t suffer “falling damage” from falling. You suffer it from landing after falling.

The damage is caused by the speed built up during the fall. Regardless, that's the word we use in English for it usually, but it could be called landing damage. Anyway, falling damage is calculated by the distance of the fall, so this Fall has no distance so if we decide to call it falling damage anyway and follow those rules it's zero damage.

However, casting Feather Fall is a reaction that you can take when you or another creature “falls,” so it was appropriate to cast it at the start of the season.

Correct. I have no issue in how the action was taken, unless he was supposed to be unaware of it.

“Falling” is the present participle, and it can be used both as an adjective (“The falling bard”) and as part of the past continuous/progress (“The bard was falling”), present continuous/progressive (“The bard is falling”), and future continuous/progressive (“The bard will be falling”) verb tenses, as well as with their perfect variants (had been falling, has been falling, will have been falling).

This is correct. Is this countering something I said or agreeing?

OK, this was too long of a reply for a stupid joke to a stupid joke...